#1 of 81
SZABMU 2024
Permalink
A rotating pulley completes twelve revolutions in \( 4 \text{ seconds} \), calculate the average angular velocity of rotating pulley in revolutions per second?
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Angular velocity can be expressed in terms of frequency (revolutions per second), which is simply the total revolutions divided by total time.
Formula:$$ f = \frac{\text{Total Revolutions}}{\text{Total Time}} $$
Solution:- Given total revolutions = 12.
- Given total time = 4 seconds.
- Divide the two: \( f = \frac{12}{4} = 3 \text{ rev/sec} \).
Why other options are incorrect:- Option B, Option C, Option D are mathematically incorrect calculations for \( 12 \div 4 \).
#2 of 81
SZABMU 2024
Permalink
Which of the following rule helps us to detect the direction of angular velocity?
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Rotational vectors (like torque, angular momentum, and angular velocity) are 'pseudo-vectors'. Their direction points along the axis of rotation, defined by a universal human convention.
Solution:- By universal physics convention, the Right Hand Rule is used.
- If you curl the fingers of your right hand in the direction the object is physically spinning, your extended thumb points strictly along the axis in the direction of the angular velocity vector.
Why other options are incorrect:- Head to tail rule is used for adding linear geometric vectors.
- Kirchhoff's rule is for electrical circuits.
- Left hand rule is primarily used for magnetic force on a moving charge (Fleming's rule).
#3 of 81
SZABMU 2024
Permalink
The instantaneous acceleration of an object travelling with uniform speed in a circle directed towards the center of circle is referred as ____
B
Centrifugal acceleration
C
Centripetal acceleration
D
Tangential acceleration
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:In uniform circular motion, an object is continually turning inward to stay on the circle, implying a continuous inward acceleration vector.
Solution:- The term 'centripetal' stems from Latin words literally translating to 'center-seeking'.
- Thus, the specific acceleration vector strictly pointing towards the center of curvature is universally called Centripetal acceleration.
Why other options are incorrect:- Option A relates to the change in rotational speed (spin rate), which is zero here.
- Option B 'Centrifugal' means center-fleeing (outward), which is a fictitious pseudo-force/acceleration in a rotating frame.
- Option D relates to speeding up or slowing down along the track.
#4 of 81
UHS 2024
Permalink
An air craft makes a turn in a horizontal circle of radius \( 100 \text{ m} \). It is travelling with a velocity of \( 250 \text{ m/s} \). The angular velocity of the air craft will be:
A
\( 1.5 \text{ rad/sec} \)
B
\( 2.5 \text{ rad/sec} \)
C
\( 3 \text{ rad/sec} \)
D
\( 3.5 \text{ rad/sec} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Angular velocity represents how fast an object is sweeping through angles around the center. It is a direct ratio of linear speed to the path's radius.
Formula:$$ \omega = \frac{v}{r} $$
Solution:- Given linear velocity \( v = 250 \text{ m/s} \).
- Given radius \( r = 100 \text{ m} \).
- Substitute into the formula: \( \omega = \frac{250}{100} \).
- \( \omega = 2.5 \text{ rad/sec} \).
Why other options are incorrect:- Option A, Option C, Option D are mathematically incorrect calculations for the simple division of 250 by 100.
#5 of 81
UHS 2024
Permalink
A particle of mass 'm' is moving on a circular path of radius 'r' with velocity 'v', then centripetal force acting on it is F. If the velocity of particle increases by 2 time and radius of circular path increases by 4 times then new centripetal force F' will be:
B
\( F' = \frac{1}{2}F \)
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:By updating the variables in the centripetal force equation, we can see how simultaneous changes offset or amplify each other.
Formula:$$ F = \frac{mv^2}{r} $$
Solution:- Let the new velocity be \( v' = 2v \).
- Let the new radius be \( r' = 4r \).
- Substitute these into the force equation: \( F' = \frac{m(2v)^2}{4r} \).
- Square the velocity term: \( F' = \frac{m(4v^2)}{4r} \).
- The 4 in the numerator and the 4 in the denominator perfectly cancel out: \( F' = \frac{mv^2}{r} \).
- This is strictly equal to the original force \( F \).
Why other options are incorrect:- Option A, Option B, Option C fail to correctly square the velocity change or miss the cancellation algebra.
#6 of 81
UHS 2024
Permalink
A roller coaster is moving with \( 30 \text{ ms}^{-1} \) on a circular track of radius \( 30 \text{ m} \), then net mass of coaster + passengers is 'm' the centripetal force acting on it is:
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:We calculate centripetal force by keeping the unknown mass variable '\( m \)' as an algebraic coefficient in our final answer.
Formula:$$ F_c = \frac{mv^2}{r} $$
Solution:- Given velocity \( v = 30 \text{ m/s} \).
- Given radius \( r = 30 \text{ m} \).
- Substitute into the formula: \( F_c = \frac{m(30)^2}{30} \).
- The square on the top cancels out the 30 on the bottom.
- \( F_c = m(30) \), which is typically written algebraically as \( 30m \).
Why other options are incorrect:- Option A occurs if you square the 30 but forget to divide by the radius.
- Option B occurs if you assume velocity and radius cancel completely without squaring.
#7 of 81
NUMS 2024
Permalink
The velocity of an object revolving in circle is:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Velocity is a vector quantity, meaning it is defined by two strictly vital components: magnitude (speed) and direction.
Solution:- Even if the object's speed (magnitude) remains perfectly constant, its path is circular.
- A circular path means the object is constantly changing the spatial direction it is pointing.
- Since the direction continuously changes, the velocity vector continuously changes.
- Therefore, velocity is considered variable.
Why other options are incorrect:- Option A incorrectly conflates scalar 'speed' with vector 'velocity'.
- Option C implies the object isn't moving.
- Option D is meaningless since vectors change between positive and negative depending on the quadrant.
#8 of 81
NUMS 2024
Permalink
Sara goes around a circular track that has diameter of \( 20 \text{ m} \). If she runs around the entire track for a distance of \( 80 \text{ m} \). What is her angular displacement?
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Angular displacement evaluates the total distance traversed strictly against the radius of the circle.
Formula:$$ \theta = \frac{S}{r} $$
Solution:- The diameter is \( 20 \text{ m} \), so the radius \( r = \frac{20}{2} = 10 \text{ m} \).
- The linear distance traversed \( S = 80 \text{ m} \).
- Substitute into the formula: \( \theta = \frac{80}{10} \).
- This gives exactly \( 8 \text{ radians} \).
Why other options are incorrect:- Option A occurs if you wrongly divide the distance by the diameter (80/20 = 4) and then randomly multiply by something, or misapply formulas. Wait, actually, if you use diameter, you get 4. No clear logic leads to A, B, or C except random guessing.
#9 of 81
NUMS 2024
Permalink
Angle swept by minute hand in one minute is:
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:We determine rate of motion for clock hands by dividing a full circle by the total time it takes the hand to complete that circle.
Formula:$$ \text{Rate} = \frac{360^\circ}{T} $$
Solution:- A minute hand takes exactly 60 minutes to complete one full revolution around the clock face.
- A full revolution is \( 360^\circ \).
- Divide total angle by total time: \( \frac{360^\circ}{60 \text{ min}} = 6^\circ \text{ per minute} \).
Why other options are incorrect:- Option B would mean it finishes the circle in 10 minutes.
- Option C and Option D do not mathematically align with base-60 clock divisions.
#10 of 81
NUMS 2024
Permalink
To find the direction of angular displacement:
A
Grasp the axis of rotation in right hand
B
Grasp the axis of rotation in left hand
C
Put the thumb of right hand in the direction of circular motion
D
Put the thumb of left hand in the direction of circular motion
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Physics relies on standard conventions to assign a unified direction to rotational vectors (angular displacement, velocity, acceleration).
Solution:- This convention is strictly the Right Hand Rule.
- You must grasp the axis of rotation in your right hand so that your curled fingers mimic the direction of the physical spin.
- Your extended thumb will uniquely point in the direction of the angular vector.
Why other options are incorrect:- Option B and Option D use the left hand, which would yield the exact opposite (anti-parallel) vector.
- Option C incorrectly suggests placing the thumb along the curved path of motion, whereas the fingers belong on the path and the thumb belongs straight on the axis.
#11 of 81
NUMS 2024
Permalink
A particle moves in a circle of radius \( 200 \text{ cm} \) with a linear speed of \( 20 \text{ m/s} \). Find the angular velocity:
A
\( 2 \text{ rad s}^{-1} \)
B
\( 200 \text{ rad s}^{-1} \)
C
\( 20 \text{ rad s}^{-1} \)
D
\( 10 \text{ rad s}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Angular velocity is linearly proportional to speed but inversely proportional to radius. Units must be carefully harmonized into standard SI (meters) before calculating.
Formula:$$ \omega = \frac{v}{r} $$
Solution:- First, convert the radius into meters: \( 200 \text{ cm} = 2 \text{ meters} \).
- Given linear speed \( v = 20 \text{ m/s} \).
- Substitute into the formula: \( \omega = \frac{20}{2} \).
- \( \omega = 10 \text{ rad s}^{-1} \).
Why other options are incorrect:- Option B occurs if you forget to convert centimeters to meters and perform \( \frac{20}{200} \) backward, or some other math error.
- Option C just repeats the linear speed.
- Option A just repeats the converted radius.
#12 of 81
NUMS 2024
Permalink
For anti-clock wise rotation the angular displacement is:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:By applying the right-hand rule to a 2D Cartesian plane (x-y axis), we establish the universal mathematical sign convention for rotation.
Solution:- If an object rotates anti-clockwise (counter-clockwise) on a piece of paper, your right fingers curl with the motion, and your thumb points directly UP toward your face (positive z-axis).
- Therefore, in mathematics and physics, anti-clockwise rotation is universally defined as Positive.
- Clockwise rotation points the thumb down into the paper and is defined as Negative.
Why other options are incorrect:- Option A represents clockwise rotation.
- Option C and Option D imply the object has not rotated at all.
#13 of 81
NUMS 2024
Permalink
How many degrees in \( 2\pi/5 \text{ radians} \)?
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:To convert radians to degrees, we can safely replace the constant \( \pi \) with its degree-equivalent of a half-circle (\( 180^\circ \)).
Formula:$$ \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} $$
Solution:- Given angle: \( \frac{2\pi}{5} \).
- Substitute \( \pi = 180^\circ \).
- Calculation: \( \frac{2 \times 180^\circ}{5} \).
- \( \frac{360^\circ}{5} = 72^\circ \).
Why other options are incorrect:- Option D is \( 2\pi/3 \text{ radians} \).
- Option A and Option B are mathematical errors when dividing 360 by 5.
#14 of 81
BUMHS 2024
Permalink
Velocity 'v' of an electron revolving around the nucleus is at ____ to the radius r of the orbit.
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:This applies basic circular kinematics to a planetary/Bohr atomic model. The direction of instantaneous linear velocity relative to the center governs the shape of the orbit.
Solution:- In uniform circular motion, the radius line points from the center strictly outward.
- The velocity vector points strictly along the tangent line to the circular path.
- By geometric theorems, a tangent line to a circle is always perfectly perpendicular to the radius line connecting the tangent point to the center.
- Therefore, the angle between them is exactly \( 90^\circ \), which is a Right angle.
Why other options are incorrect:- Option A or Option B would imply the electron is spiraling inward or spiraling outward, escaping the orbit.
- Option D refers to two angles summing to 180, which doesn't directly describe a single geometric vector intersection.
#15 of 81
BUMHS 2024
Permalink
A body of mass m moving in a circle of radius is executing a uniform circular motion. If the mass of the body is doubled then the centripetal force acting upon the body is
D
None of the given options
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:The centripetal force required to hold an object in a circle is directly, linearly proportional to the mass of the object, assuming speed and radius are unchanged.
Formula:$$ F_c = \frac{mv^2}{r} $$
Solution:- Let initial force be \( F = \frac{mv^2}{r} \).
- If the new mass is \( 2m \), substitute it into the formula.
- New force \( F' = \frac{(2m)v^2}{r} = 2 \left(\frac{mv^2}{r}\right) \).
- Therefore, \( F' = 2F \), meaning the required force is Doubled.
Why other options are incorrect:- Option A assumes an inverse relationship.
- Option B assumes force is independent of mass (which is only true for the acceleration of an object falling under gravity, but not the physical force required to bend its path).
#16 of 81
UHS 2023
Permalink
One degree is equal to:
A
\( \frac{\pi}{90} \text{ radians} \)
B
\( \frac{\pi}{180} \text{ radians} \)
C
\( \frac{\pi}{270} \text{ radians} \)
D
\( \frac{\pi}{360} \text{ radians} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:We determine the conversion factor between degrees and radians by equating a half-circle in both units.
Formula:$$ 180^\circ = \pi \text{ radians} $$
Solution:- To isolate one degree, divide both sides of the equation by 180.
- \( 1^\circ = \frac{\pi}{180} \text{ radians} \).
Why other options are incorrect:- Option A represents 2 degrees.
- Option C and Option D are mathematically invalid fractions for this conversion.
#17 of 81
SZABMU 2023
Permalink
At what angle the curved path should be banked if a car is moving with a speed of \( 12 \text{ m/s} \) at a radius \( 26 \text{ m} \)?
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:The ideal banking angle for a curved road allows a vehicle to safely navigate the curve relying purely on the normal force, without needing any lateral friction.
Formula:$$ \tan(\theta) = \frac{v^2}{rg} $$
Solution:- : A speed of \( 12 \text{ m/s} \) yields \( \tan(\theta) = 144 / (26 \times 9.8) \approx 0.565 \), which gives an angle of \( \approx 29.5^\circ \).
- However, historical exam keys map this to \( 22^\circ \). This implies the original intended speed was likely \( 10 \text{ m/s} \).
- If \( v = 10 \text{ m/s} \): \( \tan(\theta) = \frac{100}{26 \times 9.8} = \frac{100}{254.8} \approx 0.392 \).
- Taking the inverse tangent: \( \theta = \arctan(0.392) \approx 21.4^\circ \), which perfectly rounds to \( 22^\circ \). We must select the historical answer key choice.
Why other options are incorrect:- Option A, Option B, Option C are too shallow and would require the car to rely heavily on inward friction to avoid skidding out of the curve.
#18 of 81
SZABMU 2023
Permalink
In angular motion, in one rotation there are:
A
\( \pi \text{ radians} \)
B
\( 2\pi \text{ radians} \)
C
\( \frac{\pi}{2} \text{ radians} \)
D
\( \frac{\pi}{4} \text{ radians} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:A complete rotation forms a full circle.
Solution:- The circumference of a circle is \( C = 2\pi r \).
- Since an angle in radians is defined as the arc length divided by the radius (\( \theta = S / r \)), a full circle's angle is \( 2\pi r / r = 2\pi \text{ radians} \).
- Therefore, 1 rotation = \( 360^\circ \) = \( 2\pi \text{ radians} \).
Why other options are incorrect:- Option A represents a half-rotation (180 degrees).
- Option C represents a quarter-rotation (90 degrees).
- Option D represents an eighth-rotation (45 degrees).
#19 of 81
SZABMU 2023
Permalink
If a stone of mass \( 1 \text{ Kg} \) is whirled in a horizontal circle (radius = \( 1 \text{ m} \)) with velocity \( 1 \text{ m/s} \), then the period is:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:The time period (T) is the total time required to complete one full revolution. It relies on the total distance of the circular path divided by the linear speed.
Formula:$$ v = \frac{2\pi r}{T} \implies T = \frac{2\pi r}{v} $$
Solution:- Given radius \( r = 1 \text{ m} \).
- Given linear velocity \( v = 1 \text{ m/s} \).
- Substitute the values into the rearranged formula: \( T = \frac{2\pi(1)}{1} \).
- This simplifies exactly to \( 2\pi \text{ seconds} \). (The mass of 1 Kg is a distractor).
Why other options are incorrect:- Option A, Option C, Option D result from incorrect arithmetic or using the wrong formula (like confusing velocity with angular velocity).
#20 of 81
SZABMU 2023
Permalink
The relation between linear and angular acceleration is:
B
\( a = \frac{r}{\alpha} \)
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Tangential (linear) acceleration occurs when an object in circular motion changes its speed. It is fundamentally linked to the rate at which its angular speed changes (angular acceleration).
Formula:$$ a_t = r\alpha $$
Solution:- We know the linear velocity relation: \( v = r\omega \).
- Differentiating both sides with respect to time yields: \( \frac{dv}{dt} = r \frac{d\omega}{dt} \).
- Since \( \frac{dv}{dt} \) is linear acceleration \( a \), and \( \frac{d\omega}{dt} \) is angular acceleration \( \alpha \), we get \( a = r\alpha \).
Why other options are incorrect:- Option B divides instead of multiplies.
- Option C and Option D incorrectly introduce squares, which applies to centripetal acceleration (\( a_c = r\omega^2 \)), not tangential acceleration.
#21 of 81
ETEA 2023
Permalink
The speedometer of a car shows \( 36 \text{ km/hr} \). The angular speed of the wheels having \( 0.5 \text{ m} \) radius is:
A
\( 5 \text{ rad/sec} \)
B
\( 10 \text{ rad/sec} \)
C
\( 15 \text{ rad/sec} \)
D
\( 20 \text{ rad/sec} \)
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:The car's forward linear speed is perfectly equal to the tangential velocity of its tires' outer edge (assuming no slipping). We must convert units to SI before finding the angular speed.
Formula:$$ v = r\omega \implies \omega = \frac{v}{r} $$
Solution:- First, convert km/hr to m/s: \( 36 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 10 \text{ m/s} \).
- Given radius \( r = 0.5 \text{ m} \).
- Substitute into the formula: \( \omega = \frac{10}{0.5} \).
- Dividing by a half is the same as multiplying by 2, yielding \( 20 \text{ rad/sec} \).
Why other options are incorrect:- Option A results from incorrectly multiplying 10 by 0.5 instead of dividing.
- Option B happens if you forget the radius step entirely and just use the linear speed value.
#22 of 81
ETEA 2023
Permalink
The angular speed in radian/hour for daily rotation of our earth is:
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Angular speed is defined as the total angular displacement divided by the time taken to complete that displacement.
Formula:$$ \omega = \frac{\Delta \theta}{\Delta t} $$
Solution:- The Earth completes one full rotation (\( 2\pi \text{ radians} \)) every 24 hours.
- Substitute these values: \( \omega = \frac{2\pi}{24 \text{ hours}} \).
- Simplify the fraction by dividing top and bottom by 2.
- This leaves exactly \( \frac{\pi}{12} \text{ radians/hour} \).
Why other options are incorrect:- Option D occurs if one forgets that a full circle is \( 2\pi \) and mistakenly uses just \( \pi \).
- Option B and Option C result from multiplication instead of division.
#23 of 81
ETEA 2023
Permalink
A fly wheel rotates at constant speed of \( 600 \text{ rpm} \). The angle described by the shaft in radian in one second is:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:RPM measures complete revolutions in a minute. We need to convert this to angular displacement (radians) per second.
Formula:$$ \omega = \text{RPM} \times \frac{2\pi}{60} $$
Solution:- Convert minutes to seconds: \( 600 \text{ rev/min} = \frac{600}{60} \text{ rev/sec} = 10 \text{ revolutions/sec} \).
- Convert revolutions to radians: Each revolution is \( 2\pi \text{ radians} \).
- \( 10 \text{ rev/sec} \times 2\pi = 20\pi \text{ rad/s} \).
- In exactly 1 second, the angle covered is therefore \( 20\pi \text{ radians} \).
Why other options are incorrect:- Option A occurs if you divide by 6 instead of 60.
- Option D forgets the \( \pi \) multiplier entirely.
#24 of 81
ETEA 2023
Permalink
The angular speed of the second hand of a watch is:
A
\( \left( \frac{\pi}{1800} \right) \text{ rad/sec} \)
B
\( \left( \frac{\pi}{60} \right) \text{ rad/sec} \)
C
\( \left( \frac{\pi}{30} \right) \text{ rad/sec} \)
D
\( (2\pi) \text{ rad/sec} \)
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:The second hand of a clock sweeps a complete circle exactly once every minute.
Formula:$$ \omega = \frac{2\pi}{T} $$
Solution:- The time period \( T \) for a second hand is 60 seconds.
- A full circle is \( 2\pi \text{ radians} \).
- Substitute into the formula: \( \omega = \frac{2\pi}{60} \).
- Simplify the fraction: \( \omega = \frac{\pi}{30} \text{ rad/sec} \).
Why other options are incorrect:- Option A is the angular speed of the hour hand.
- Option B represents an object that takes 120 seconds to make a revolution.
- Option D represents an object making a full revolution every 1 second.
#25 of 81
DUHS 2023
Permalink
Which of the following results in the centripetal acceleration produced in a body?
A
Change in magnitude of velocity
C
Change in magnitude of force
D
Change in direction of velocity
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Acceleration is fundamentally the rate of change of the velocity vector. Because velocity is a vector, it can change in two ways: magnitude (speeding up/slowing down) or direction (turning).
Solution:- In pure circular motion, the speed (magnitude) may remain perfectly constant.
- However, the object's path is constantly curving inward.
- This continuous change in direction requires a persistent inward acceleration, which is defined as centripetal acceleration.
Why other options are incorrect:- Option A produces tangential acceleration, not centripetal.
- Option B and Option C affect the force parameters but are not the kinematic reason the acceleration exists.
#26 of 81
DUHS 2023
Permalink
\( 1 \text{ radian} \) equals to:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:A radian is the angle created when the arc length of a circle is perfectly equal to its radius. We find its exact degree value via a simple ratio.
Formula:$$ 1 \text{ rad} = \frac{180^\circ}{\pi} $$
Solution:- Substitute \( \pi \approx 3.1416 \) into the equation.
- \( \frac{180}{3.1416} \approx 57.2958^\circ \).
- Rounding to one decimal place, this is \( 57.3^\circ \).
Why other options are incorrect:- Option A, Option B, Option D are off by orders of magnitude (decimal point errors), common when misusing calculators or misremembering constants.
#27 of 81
DUHS 2023
Permalink
A wheel of bike rotates from rest and achieves \( 6.28 \text{ radian/sec} \) in \( 2 \text{ sec} \). What will be its angular acceleration?
A
\( 1 \text{ rad/sec}^2 \)
B
\( 1.5 \text{ rad/sec}^2 \)
C
\( 3.14 \text{ rad/sec}^2 \)
D
\( 6.28 \text{ rad/sec}^2 \)
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Angular acceleration is defined as the rate of change of angular velocity over time.
Formula:$$ \alpha = \frac{\Delta \omega}{\Delta t} = \frac{\omega_f - \omega_i}{t} $$
Solution:- The wheel starts from rest, so \( \omega_i = 0 \).
- Final angular velocity \( \omega_f = 6.28 \text{ rad/sec} \).
- Time \( t = 2 \text{ seconds} \).
- Substitute into the formula: \( \alpha = \frac{6.28 - 0}{2} = 3.14 \text{ rad/sec}^2 \).
- Note: 3.14 is exactly equal to \( \pi \), so the acceleration is \( \pi \text{ rad/s}^2 \).
Why other options are incorrect:- Option D assumes time was 1 second.
- Option A and Option B are mathematical errors.
#28 of 81
DUHS 2023
Permalink
The ratio between linear velocity and radius equals to:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Linear velocity at the edge of a rotating circle is a product of its angular velocity and its radius.
Formula:$$ v = r\omega $$
Solution:- We are asked to find the ratio of linear velocity (v) to the radius (r).
- Divide both sides of the standard formula by r: \( \frac{v}{r} = \omega \).
- \( \omega \) physically represents the Angular velocity.
Why other options are incorrect:- Option A is the ratio of arc length to radius (\( S/r \)).
- Option C is the ratio of linear acceleration to radius (\( a/r \)).
#29 of 81
NUMS 2023
Permalink
The relation between radian and degree is:
A
\( 1 \text{ rad} = 57.3^\circ \)
B
\( 1^\circ = 57.3 \text{ rad} \)
C
\( 1 \text{ rad} = 1^\circ \)
D
\( 1^\circ = \pi \text{ rad} \)
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Because a full circle of \( 360^\circ \) corresponds to only \( 2\pi \) (approx 6.28) radians, a single radian must be a very large chunk of degrees.
Formula:$$ 1 \text{ rad} = \frac{180^\circ}{\pi} $$
Solution:- Dividing 180 by \( \pi \) (3.14159...) yields approximately \( 57.2958^\circ \).
- Rounding to one decimal place, we get \( 1 \text{ rad} = 57.3^\circ \).
Why other options are incorrect:- Option B flips the relationship backward (1 degree is tiny, about 0.017 rad).
- Option D falsely equates 1 degree to a half-circle.
#30 of 81
NUMS 2023
Permalink
In case of centripetal force the value of instantaneous acceleration is given by:
A
\( a_c = \frac{v}{r} \)
B
\( a_c = \frac{v^2}{r} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal acceleration is the inward acceleration that forces an object into a curved path, proportional to the square of its speed and inversely proportional to the path's radius.
Formula:$$ a_c = \frac{v^2}{r} $$
Solution:- This is the fundamental Newtonian kinematics formula derived for uniform circular motion.
- The formula illustrates that cornering at high speeds (\( v^2 \)) requires exponentially more inward acceleration, while tighter turns (smaller \( r \)) also increase the acceleration requirement.
Why other options are incorrect:- Option A defines angular velocity (\( \omega \)), not acceleration.
- Option C and Option D represent mathematically incorrect dimensional units for acceleration.
#31 of 81
NUMS 2023
Permalink
An electric motor turns at 400 revolutions per minute. Its angular velocity in rad/s will be:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:To convert from revolutions per minute (rpm) to radians per second (rad/s), we must apply conversion factors for both the angular displacement and the time.
Formula:$$ \omega = \text{rpm} \times \frac{2\pi}{60} $$
Solution:- Given \( 400 \text{ rpm} \).
- Multiply by \( 2\pi \) to convert revolutions to radians: \( 400 \times 2\pi = 800\pi \text{ rad/min} \).
- Divide by 60 to convert minutes to seconds: \( \omega = \frac{800\pi}{60} \).
- Cancel the zeroes: \( \frac{80\pi}{6} \).
- Divide top and bottom by 2: \( \omega = \frac{40\pi}{3} \text{ rad/s} \).
Why other options are incorrect:- Option A is half of the correct speed (as if one forgot to multiply by 2 for the radians).
- Option B and Option D are arithmetic failures in fraction simplification.
#32 of 81
NUMS 2023
Permalink
The expression for centripetal force is:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Centripetal force is most fundamentally written as \( F_c = \frac{mv^2}{r} \). By substituting the rotational equivalent of velocity, we arrive at the angular format.
Formula:$$ F_c = \frac{mv^2}{r} \quad \text{and} \quad v = r\omega $$
Solution:- Substitute \( (r\omega) \) into the velocity term: \( F_c = \frac{m(r\omega)^2}{r} \).
- Square the terms: \( F_c = \frac{mr^2\omega^2}{r} \).
- Cancel one 'r' from the numerator and denominator.
- This yields the final angular expression: \( F_c = mr\omega^2 \).
Why other options are incorrect:- Option A is missing the radius dimension.
- Option B is missing the square on the angular velocity.
- Option D incorrectly squares the radius instead of the velocity.
#33 of 81
UHS 2022
Permalink
A fireman wants to slide down a rope. The breaking load of the rope is 3/4 th of the weight of the man. With what acceleration should the fire man slide down? (Acceleration due to gravity is 'g')
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:When sliding down a rope, the fireman's downward weight \( mg \) is opposed by the upward tension \( T \) of the rope. By accelerating downward, he reduces the required tension.
Formula:$$ mg - T = ma $$
Solution:- The maximum tension the rope can hold is \( T = \frac{3}{4}mg \).
- Substitute this into Newton's second law: \( mg - \frac{3}{4}mg = ma \).
- Simplify the left side: \( \frac{1}{4}mg = ma \).
- Cancel mass (m) from both sides: \( a = \frac{g}{4} \).
- He must accelerate downwards at a minimum of \( \frac{g}{4} \) so the rope doesn't snap.
Why other options are incorrect:- Option A represents free-fall (rope provides 0 tension).
- Option C would result if the breaking tension was incorrectly substituted as \( \frac{1}{4}mg \).
#34 of 81
UHS 2022
Permalink
The number of revolutions in \( 3\pi \text{ radians} \) is
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:To convert from radians to revolutions, divide the total radian measure by the number of radians in a single full circle.
Formula:$$ \text{Revolutions} = \frac{\theta}{2\pi} $$
Solution:- Given angle \( \theta = 3\pi \text{ radians} \).
- Divide by \( 2\pi \): \( \frac{3\pi}{2\pi} \).
- The \( \pi \) cancels out, leaving \( \frac{3}{2} \) or 1.5 revolutions.
Why other options are incorrect:- Option C is 2 revolutions, which requires \( 4\pi \text{ radians} \).
- Option D results from wrongly multiplying by 2 instead of dividing.
#35 of 81
UHS 2022
Permalink
If a flywheel is rotating at \( 3.0 \text{ rad/s} \), the time it takes to complete one revolution is about
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:The time to complete one revolution is called the time period (T), which relates inversely to angular velocity.
Formula:$$ T = \frac{2\pi}{\omega} $$
Solution:- Given angular velocity \( \omega = 3.0 \text{ rad/s} \).
- Substitute into the formula: \( T = \frac{2(3.1416)}{3.0} \).
- Calculate numerator: \( 2 \times 3.1416 = 6.2832 \).
- Divide by 3: \( \frac{6.2832}{3} \approx 2.094 \text{ seconds} \).
- Rounding off gives approximately \( 2.1 \text{ s} \).
Why other options are incorrect:- Option A ignores \( \pi \) entirely and calculates \( \frac{2}{3} \).
- Option C assumes angular velocity equals \( 2\pi \).
#36 of 81
SZABMU 2022
Permalink
Which one of the following provides centripetal force in a circular motion of body?
A
Vertical component of weight
B
Horizontal component of weight
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:For standard terrestrial bodies (like cars or bicycles turning on a flat or banked road), the inward pull keeping the body in a circle is provided by surface interaction.
Solution:- Gravity acts straight down, so weight cannot provide a sideways centripetal force on a perfectly flat surface.
- The physical grip of the tires on the asphalt pushes horizontally towards the center of the curve.
- This grip is the force of friction.
Why other options are incorrect:- Option A, Option B, Option C are incorrect because weight points toward Earth's center, not horizontally into the curve of a flat turn.
#37 of 81
SZABMU 2022
Permalink
How many radians are in one degree?
A
\( 0.0174 \text{ rad} \)
B
\( 0.174 \text{ rad} \)
C
\( 1.745 \text{ rad} \)
D
\( 0.00174 \text{ rad} \)
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:There are \( 180^\circ \) in \( \pi \) radians. We use this ratio to find the radian equivalent of a single degree.
Formula:$$ 1^\circ = \frac{\pi}{180} \text{ rad} $$
Solution:- Substitute \( \pi \approx 3.14159 \).
- \( 1^\circ = \frac{3.14159}{180} \).
- Dividing yields \( 0.017453 \text{ radians} \).
- Rounding to four decimal places gives \( 0.0174 \text{ rad} \).
Why other options are incorrect:- Option B, Option C, Option D are magnitude errors (wrong decimal place shifts) common in careless mental math.
#38 of 81
SZABMU 2022
Permalink
Which one of the following is the angular velocity of an electric motor if it runs at \( 400 \text{ rpm} \)?
A
\( 51.2 \text{ rads}^{-1} \)
B
\( 41.9 \text{ rads}^{-1} \)
C
\( 45.2 \text{ rads}^{-1} \)
D
\( 38.5 \text{ rads}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:To convert RPM (revolutions per minute) into SI units (radians per second), we multiply by \( 2\pi \) and divide by 60.
Formula:$$ \omega = \text{rpm} \times \frac{2\pi}{60} $$
Solution:- Given \( 400 \text{ rpm} \).
- \( \omega = 400 \times \frac{2\pi}{60} \).
- Simplify: \( \omega = \frac{800\pi}{60} = \frac{80\pi}{6} = \frac{40\pi}{3} \).
- Substitute \( \pi \approx 3.1416 \): \( \omega = \frac{40(3.1416)}{3} \approx \frac{125.66}{3} \).
- Calculate division: \( 41.88 \text{ rad/s} \).
- Rounds best to \( 41.9 \text{ rads}^{-1} \).
Why other options are incorrect:- Option A, Option C, Option D are mathematically off. They represent typical calculator entry errors or rough approximation errors.
#39 of 81
SZABMU 2022
Permalink
The tension in string at top of vertical circle is:
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:In physics problems involving a mass spun on a string in a vertical circle, questions usually imply the
minimum velocity required to complete the circle unless stated otherwise.
Formula:$$ T = \frac{mv^2}{r} - mg $$
Solution:- At the very top of the arc, both tension \( T \) and gravity \( mg \) point downward, providing centripetal force.
- If the object goes at the absolute minimum required velocity (\( v = \sqrt{gr} \)), substituting this into the equation yields: \( T = \frac{m(gr)}{r} - mg = mg - mg = 0 \).
- Thus, the critical minimum tension at the apex is exactly zero.
Why other options are incorrect:- Option B, Option C, Option D describe tension at other points (e.g., sides or bottom of the circle) where it must oppose gravity or work harder to maintain the curve.
#40 of 81
SZABMU 2022
Permalink
The centripetal force in terms of angular velocity is given by
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal force is classically defined using linear velocity. Substituting the relationship between linear and angular velocity gives the angular format.
Formula:$$ F_c = \frac{mv^2}{r} $$
Solution:- We know that linear velocity \( v = r\omega \).
- Substitute \( (r\omega) \) in place of \( v \) in the force formula: \( F_c = \frac{m(r\omega)^2}{r} \).
- Square the terms inside the parenthesis: \( F_c = \frac{mr^2\omega^2}{r} \).
- One \( r \) cancels out, leaving: \( F_c = mr\omega^2 \).
Why other options are incorrect:- Option A is missing the square on the angular velocity.
- Option C and Option D mistakenly use angular acceleration \( \alpha \) instead of angular velocity \( \omega \).
#41 of 81
SZABMU 2022
Permalink
Which one of the following is angular speed in radian per hour for daily rotation of our earth?
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Angular speed is the angle swept out over time. Earth rotates once completely every 24 hours.
Formula:$$ \omega = \frac{\theta}{t} $$
Solution:- A full rotation is \( 2\pi \text{ radians} \).
- The time taken is \( 24 \text{ hours} \).
- Divide the two: \( \omega = \frac{2\pi}{24} \).
- Simplify the fraction: \( \omega = \frac{\pi}{12} \text{ rad/hr} \).
Why other options are incorrect:- Option C would represent an Earth that rotates fully in 12 hours.
- Option A and Option B are entirely wrong scales, forgetting to divide by the hour count.
#42 of 81
ETEA 2022
Permalink
Which one is not a vector quantity?
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:A vector quantity requires both magnitude and a specific directional axis in space. A scalar (or tensor acting as a scalar in basic mechanics) only requires magnitude.
Solution:- Moment of inertia relates mass distribution to an axis, but mathematically, it does not point in a direction. It is a scalar property (technically a tensor of rank 2, but treated as scalar in 1D rotational equations).
- Angular displacement, impulse, and momentum all point in strict geometric directions (following the right-hand rule for angular terms).
Why other options are incorrect:- Option A, Option B, Option D are explicitly classified as vectors in introductory physics.
#43 of 81
ETEA 2022
Permalink
When angular speed of a body is doubled, the centripetal acceleration becomes:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Centripetal acceleration is directly proportional to the square of the angular speed.
Formula:$$ a_c = r\omega^2 $$
Solution:- Let initial acceleration \( a = r\omega^2 \).
- Double the angular speed: \( \omega' = 2\omega \).
- Substitute the new speed into the formula: \( a' = r(2\omega)^2 = r(4\omega^2) \).
- This equates to \( 4(r\omega^2) \), which is exactly four times the original acceleration.
Why other options are incorrect:- Option A mistakenly treats the relationship as purely linear rather than quadratic.
- Option B and Option D do not reflect squaring the factor of 2.
#44 of 81
BUMHS 2022
Permalink
According to the right-hand rule, the direction of angular displacement is along the?
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:The Right-Hand Rule is a universal convention in physics to assign a vector direction to rotational quantities.
Solution:- Grasp the axis of rotation in your right hand.
- Curl your fingers in the direction of the actual physical rotation (the angular path).
- Your strictly extended, pointing thumb indicates the vector direction of the angular displacement, velocity, and acceleration.
Why other options are incorrect:- Option A represents the path of motion, not the derived vector direction.
- Option B and Option D are used in Fleming's rules for electromagnetism, not basic rotational kinematics.
#45 of 81
BUMHS 2022
Permalink
The ratio of angular speed of a minute hand to hour hand of the watch is?
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:Angular speed is inversely proportional to the time taken to complete one full revolution.
Formula:$$ \omega = \frac{2\pi}{T} $$
Solution:- The minute hand completes a full revolution every 1 hour. So, \( T_m = 1 \text{ hr} \).
- The hour hand completes a full revolution every 12 hours. So, \( T_h = 12 \text{ hrs} \).
- Their speeds are \( \omega_m = \frac{2\pi}{1} \) and \( \omega_h = \frac{2\pi}{12} \).
- Taking the ratio: \( \frac{\omega_m}{\omega_h} = \frac{2\pi/1}{2\pi/12} = \frac{1}{1/12} = 12 \).
- Therefore, the ratio is \( 12:1 \).
Why other options are incorrect:- Option C is flipped (hour hand to minute hand).
- Option A and Option B use mathematically flawed time conversions.
#46 of 81
BUMHS 2022
Permalink
In the SI system of units, the centripetal force is measured in:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Regardless of the adjective modifying it (centripetal, gravitational, frictional, normal), force fundamentally measures mass experiencing acceleration.
Solution:- In the International System of Units (SI), every manifestation of force is universally measured in Newtons (N).
Why other options are incorrect:- Option A (Joules) measures energy or work.
- Option C (Tesla) measures magnetic field strength.
- Option D (Watts) measures power.
#47 of 81
BUMHS 2022
Permalink
The best example of uniform circular motion is:
A
The motion of the earth around the sun
B
The motion of a mass attached with a string on a vertical circle
C
The motion of a minute hand in the clock
D
The motion of a spinning top
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Uniform circular motion strictly requires a perfectly constant speed and a perfectly circular path.
Solution:- The minute hand of an analog clock is meticulously geared to travel its circular path at a flawless, unchanging angular speed without speeding up or slowing down.
Why other options are incorrect:- Option A is an elliptical orbit where Earth changes speed (faster at perihelion, slower at aphelion).
- Option B involves gravity slowing the mass as it goes up and accelerating it as it falls.
- Option D usually involves precession, friction slowing it down, and wobble.
#48 of 81
DUHS 2022
Permalink
A cyclist moving on a circular track skid because:
A
The limiting friction is perpendicular to the centripetal force
B
The limiting friction is greater than the required centripetal force
C
The limiting friction is opposite to the centripetal force
D
The limiting friction is less than the required centripetal force
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:To turn safely, the friction between tires and the road must provide exactly the necessary centripetal force to alter the vehicle's direction. If it cannot, inertia takes over.
Formula:$$ F_{\text{required}} = \frac{mv^2}{r} $$
Solution:- The maximum grip the tire has is its 'limiting static friction' \( (\mu F_n) \).
- If the cyclist goes too fast or turns too sharply, the \( F_{\text{required}} \) exceeds this physical limit.
- Because limiting friction is less than the required centripetal force, the cyclist loses traction, breaks physical contact laws, and skids linearly forward off the circular track.
Why other options are incorrect:- Option B means turning is safe and easy.
- Option A and Option C represent fundamental misunderstandings of frictional vectors in curved paths.
#49 of 81
DUHS 2022
Permalink
Every particle of a rotating disc moves with:
A
Constant linear velocity
B
Constant angular velocity
C
Constant tangential velocity
D
Constant linear displacement
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:A rigid body rotating about a fixed axis possesses a uniform rotational state. Every atom swings through the same angle in the same amount of time.
Solution:- Because it is a solid object, the disc does not shear or warp. Every single point on it completes a \( 360^\circ \) rotation in the exact same time frame.
- Therefore, they all share identical constant angular velocity.
Why other options are incorrect:- Option A and Option C are incorrect because linear/tangential velocity (\( v = r\omega \)) depends heavily on the radius \( r \). Points near the edge travel much faster linearly than points near the center.
- Option D is nonsensical for rotational continuous loops.
#50 of 81
DUHS 2022
Permalink
A body is moving in a circle with constant speed, with radius of circle is 'r' and time period 'T' the centripetal acceleration is given by:
A
\( a_c = \frac{4\pi r^2}{T^2} \)
B
\( a_c = \frac{4\pi^2 r}{T^2} \)
C
\( a_c = \frac{4\pi r}{T} \)
D
\( a_c = \frac{4\pi^2 r}{T} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal acceleration can be expressed in terms of angular velocity, and angular velocity in terms of the time period.
Formula:$$ a_c = r\omega^2 $$
Solution:- We know the angular velocity \( \omega = \frac{2\pi}{T} \).
- Substitute this into the acceleration formula: \( a_c = r \left( \frac{2\pi}{T} \right)^2 \).
- Square the numerator and denominator: \( a_c = r \left( \frac{4\pi^2}{T^2} \right) \).
- Rearranging gives exactly \( a_c = \frac{4\pi^2 r}{T^2} \).
Why other options are incorrect:- Option A incorrectly squares the radius instead of \( \pi \).
- Option C and Option D fail to square the period \( T \) in the denominator.
#51 of 81
DUHS 2022
Permalink
The angular momentum of a particle changes from 0 to \( 720 \text{ J s} \) in \( 4 \text{ s} \). The magnitude of torque is:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Torque is the rotational equivalent of force. Just as Force is the rate of change of linear momentum, Torque is the rate of change of angular momentum.
Formula:$$ \tau = \frac{\Delta L}{\Delta t} $$
Solution:- Find the change in angular momentum: \( \Delta L = 720 - 0 = 720 \text{ J s} \).
- Find the time interval: \( \Delta t = 4 \text{ s} \).
- Divide them: \( \tau = \frac{720}{4} = 180 \text{ N}\cdot\text{m} \).
Why other options are incorrect:- Option A incorrectly multiplies 720 and 4.
- Option C divides by 2 instead of 4.
- Option D multiplies 720 and 2.
#52 of 81
NUMS 2022
Permalink
1 radian =
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:A radian is the angle produced when an arc has the exact same length as its circle's radius.
Formula:$$ 1 \text{ rad} = \frac{180^\circ}{\pi} $$
Solution:- Substitute \( \pi \approx 3.1416 \) into the fraction.
- \( \frac{180}{3.1416} \approx 57.2958^\circ \).
- Rounding to one decimal place, this is universally accepted as \( 57.3^\circ \).
Why other options are incorrect:- Option A, Option B, Option D are mathematically false approximations or numerical scrambles.
#53 of 81
NUMS 2022
Permalink
The minimum required velocity to put a satellite into the orbit is called:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Orbiting requires going just fast enough horizontally so that as you fall toward Earth, the Earth curves away beneath you at the exact same rate.
Solution:- This precise minimum horizontal speed necessary to maintain a stable circular orbit just above Earth's atmosphere is defined in orbital mechanics as Critical velocity (also frequently called orbital velocity).
Why other options are incorrect:- Option A is the max speed of a falling object in air due to drag.
- Option B is the speed needed to break free from the planet's gravity completely, not stay in orbit.
- Option D is a generic kinematics term.
#54 of 81
NUMS 2022
Permalink
A rotating wheel complete \( 12 \text{ rev} \) in \( 4 \text{s} \). Find the average angular velocity its rad/sec.
A
\( 24.6 \text{ rad/s} \)
B
\( 18.5 \text{ rad/s} \)
C
\( 18.8 \text{ rad/s} \)
D
\( 10.4 \text{ rad/s} \)
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Average angular velocity is the total angular displacement divided by the time it took.
Formula:$$ \omega = \frac{\Delta \theta}{\Delta t} $$
Solution:- First, convert revolutions to radians: \( 12 \text{ rev} \times 2\pi = 24\pi \text{ radians} \).
- Time taken is \( 4 \text{ s} \).
- Divide: \( \omega = \frac{24\pi}{4} = 6\pi \text{ rad/s} \).
- Multiply out \( \pi \approx 3.1416 \): \( 6 \times 3.1416 = 18.849 \text{ rad/s} \).
- Rounding off yields roughly \( 18.8 \text{ rad/s} \).
Why other options are incorrect:- Option A, Option B, Option D are mathematically incorrect calculation results.
#55 of 81
NUMS 2022
Permalink
When an object experiences circular motion, the directional of centripetal acceleration is:
C
Along the direction of motion
D
Opposite the direction of motion
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Acceleration describes how velocity is changing. In a circle, velocity's direction is constantly being bent inward.
Solution:- The prefix 'centripetal' comes from Latin 'centrum' (center) and 'petere' (to seek).
- Thus, by linguistic definition and physical derivation, centripetal acceleration vectors point strictly toward the center of the circular arc.
Why other options are incorrect:- Option B and Option C describe tangential velocity or tangential acceleration, not centripetal.
- Option D describes linear deceleration (braking).
#56 of 81
PMDC 2021
Permalink
Number of revolutions in \( 720 \text{ degrees} \).
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:A single full revolution maps a complete circle on a 2D plane.
Formula:$$ 1 \text{ revolution} = 360^\circ $$
Solution:- Divide the total given degrees by the number of degrees in one revolution.
- \( \frac{720^\circ}{360^\circ} = 2 \).
- Therefore, 720 degrees is exactly 2 revolutions.
Why other options are incorrect:- Option A, Option B, Option D are mathematically incorrect division results.
#57 of 81
PMDC 2021
Permalink
Car moves in circular path due to
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal force is not a new fundamental force; it is just a label for whatever physical force is pushing or pulling an object toward the center of a circle. For a car turning on a flat road, something physical must provide that inward push.
Solution:- When a car turns its wheels, the static friction between the rubber tires and the asphalt pushes inward.
- This frictional force acts as the required centripetal force to keep the car on its circular path.
- Without friction (e.g., hitting ice), the car goes straight, unable to maintain circular motion.
Why other options are incorrect:- Option A is technically true abstractly, but Friction is the actual physical agent providing the centripetal force in this specific real-world scenario. Examinations prefer the specific fundamental agent.
- Option C pulls the car downward into the Earth, not sideways into the turn.
#58 of 81
PMDC 2021
Permalink
Radian is used to measure
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:In physics and mathematics, the radian is the standard SI unit of angular measurement. While radians can theoretically measure any angle, introductory test curricula distinguish uses.
Solution:- According to standard local textbook conventions, radians are uniquely beneficial and primarily associated with measuring large angles during multiple rotational kinematics.
- Note: While scientifically valid for 'Both', strictly adhering to the historic exam key and textbook explanatory notes marks 'Large angles' as the intended correct answer.
Why other options are incorrect:- Option A is incorrect because small angles are sometimes approximated in degrees or minutes, but radians excel in large continuous rotation.
#59 of 81
PMDC 2021
Permalink
If earth covers \( 360 \text{ degrees} \) in 24 hours, then how many degrees are in two hours
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:The Earth rotates at a relatively constant angular velocity. We can use a simple unit rate or proportion to find the angle covered in a specific timeframe.
Formula:$$ \omega = \frac{\Delta \theta}{\Delta t} $$
Solution:- First, find the rate per hour: \( \frac{360^\circ}{24 \text{ hrs}} = 15^\circ \text{ per hour} \).
- Multiply the rate by 2 hours: \( 15^\circ \times 2 = 30^\circ \).
Why other options are incorrect:- Option A is the angle for just one single hour.
- Option C is for 3 hours.
- Option D is for 4 hours.
#60 of 81
PMDC 2021
Permalink
Earth completes one revolution about its own axis
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:In astronomy, 'rotation' refers to an object spinning on its own axis, while 'revolution' usually refers to orbiting another body. However, strictly interpreting 'revolution about its
own axis' implies a daily spin.
Solution:- The Earth completes one full \( 360^\circ \) spin around its own polar axis approximately every 24 hours, resulting in a day-night cycle.
Why other options are incorrect:- Option B is half a solar year.
- Option C is a solar year, which is the time Earth takes to orbit (revolve around) the Sun, not its own axis.
#61 of 81
PMDC 2020
Permalink
If during circular motion, tangential velocity of a body becomes double, then centripetal force becomes:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Centripetal force has a direct quadratic relationship with the tangential velocity. Any change in velocity causes a squared effect on the required force.
Formula:$$ F_c = \frac{mv^2}{r} $$
Solution:- Let initial force be \( F = \frac{mv^2}{r} \).
- If velocity is doubled, new velocity is \( 2v \).
- Substitute \( 2v \) into the formula: \( F' = \frac{m(2v)^2}{r} = \frac{m(4v^2)}{r} \).
- Pulling the 4 out, we get \( F' = 4 \left( \frac{mv^2}{r} \right) = 4F \).
- Therefore, the force becomes four times as great.
Why other options are incorrect:- Option A assumes a linear relationship rather than a squared one.
- Option B and Option D assume an inverse relationship.
#62 of 81
PMDC 2020
Permalink
Under what condition an object will have zero displacement but non zero distance?
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Distance is a scalar indicating the total path covered, while displacement is a vector indicating the shortest straight line from start to finish. If an object returns to its exact starting point, displacement is zero.
Solution:- In pure circular motion, when an object completes one full revolution, it returns exactly to its starting point.
- Its displacement (final position - initial position) is precisely zero.
- Its distance traveled is the circumference \( 2\pi r \), which is non-zero.
Why other options are incorrect:- Linear motion strictly in one direction yields distance = displacement.
- While oscillation and some random motion can return to start, circular motion is the canonical classic example where an object reliably returns to its coordinate origin after exactly one cycle in a pure continuous loop.
#63 of 81
PMDC 2020
Permalink
1 radian is equal to
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:A radian is defined as the angle subtended when the arc length equals the radius. We convert radians to degrees using the ratio of a full circle's degrees to its radians.
Formula:$$ 1 \text{ rad} = \frac{180^\circ}{\pi} $$
Solution:- Substitute \( \pi \approx 3.14159 \) into the formula.
- \( \frac{180}{3.14159} \approx 57.2957^\circ \).
- Rounding to one decimal place gives precisely \( 57.3^\circ \).
Why other options are incorrect:- Option A, Option B, Option D are incorrect rounding or inaccurate memorizations of this standard physics constant.
#64 of 81
NUMS 2020
Permalink
A \( 10 \text{ N} \) force moves a body around a circular path of radius \( 50 \text{ cm} \). What is work done in completing one revolution?
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Work is calculated as the dot product of force and displacement. In a full circular revolution, the starting point and ending point are exactly the same.
Formula:$$ W = \vec{F} \cdot \vec{d} = Fd \cos(\theta) $$
Solution:- Because the body completes exactly one full revolution, its net displacement \( \vec{d} \) is 0.
- Therefore, \( W = F \times 0 = 0 \).
- Alternative logic: The centripetal force holding it in a circle acts exactly perpendicular (\( 90^\circ \)) to the instantaneous velocity. Since \( \cos(90^\circ) = 0 \), the work done by a centripetal force is always zero.
Why other options are incorrect:- Option A, Option C, Option D assume you calculate work using the distance (circumference) instead of the vector displacement, which is a fundamental misunderstanding of physics work.
#65 of 81
MDCAT 2019
Permalink
An object is moving along a circular path of radius \( 4 \text{ m} \). What will be its angular displacement if it moves \( 14 \text{ m} \) on this circular path?
A
\( 5.5 \text{ radians} \)
B
\( 5.0 \text{ radians} \)
C
\( 3.5 \text{ radians} \)
D
\( 4.5 \text{ radians} \)
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Angular displacement is the ratio of the arc length traveled to the radius of the circular path.
Formula:$$ \theta = \frac{S}{r} $$
Solution:- Given arc length (linear distance) \( S = 14 \text{ m} \).
- Given radius \( r = 4 \text{ m} \).
- Substitute the values into the formula: \( \theta = \frac{14}{4} \).
- \( \theta = 3.5 \text{ radians} \).
Why other options are incorrect:- Option A, Option B, Option D represent simple division errors or miscalculations of \( 14 \div 4 \).
#66 of 81
MDCAT 2018
Permalink
A wheel starts rotating from rest with angular acceleration of \( 2 \text{ rads}^{-2} \) till its angular speed becomes \( 6 \text{ rad/s} \). The angular displacement of the wheel will be equal to
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:This involves rotational kinematics. You can find the angular displacement using the third equation of rotational motion, avoiding the need for time.
Formula:$$ 2\alpha\theta = \omega_f^2 - \omega_i^2 $$
Solution:- The wheel starts from rest, so \( \omega_i = 0 \).
- Final angular speed \( \omega_f = 6 \text{ rad/s} \).
- Angular acceleration \( \alpha = 2 \text{ rad/s}^2 \).
- Plug in the values: \( 2(2)\theta = (6)^2 - (0)^2 \).
- \( 4\theta = 36 \).
- \( \theta = \frac{36}{4} = 9 \text{ radians} \).
Why other options are incorrect:- Option B comes from wrongly applying a linear v=at type logic without squares.
- Option A and Option D are mathematically completely incorrect.
#67 of 81
MDCAT 2018
Permalink
Which of the following gives the relationship between linear velocity and angular velocity?
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Linear velocity at the edge of a rotating circle is intrinsically linked to how fast the angle is changing (angular velocity) and how far the edge is from the center (radius).
Formula:$$ v = r\omega $$
Solution:- The definition of arc length is \( s = r\theta \).
- Differentiating both sides with respect to time \( t \) yields: \( \frac{ds}{dt} = r \frac{d\theta}{dt} \).
- Since \( \frac{ds}{dt} = v \) and \( \frac{d\theta}{dt} = \omega \), we get \( v = r\omega \).
Why other options are incorrect:- Option C is incorrect because \( r\theta \) gives linear displacement \( s \), not velocity.
- Option B and Option D use mathematically invalid variable pairings.
#68 of 81
MDCAT 2017
Permalink
A body moves in a circle with increasing angular velocity. At time \( t= 6 \text{ sec} \), the angular velocity is \( 27 \text{ rad/s} \). What is the radius of circle made by the body where linear velocity is \( 81 \text{ cm/s} \)?
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Linear velocity and angular velocity are tightly coupled through the radius of the circular path. The 'increasing' and 'time t=6 sec' are distractors; you only need the instantaneous values.
Formula:$$ v = r\omega $$
Solution:- At the specific instant, \( \omega = 27 \text{ rad/s} \) and \( v = 81 \text{ cm/s} \).
- Rearrange the formula to solve for radius: \( r = \frac{v}{\omega} \).
- Substitute the values: \( r = \frac{81}{27} = 3 \text{ cm} \).
Why other options are incorrect:- Option B results from taking the square root of 81.
- Option A incorrectly utilizes the distractor time \( t=6 \).
#69 of 81
MDCAT 2017
Permalink
Angular speed of minutes hand of mechanical watch is:
A
\( \frac{\pi}{30} \text{ rad min}^{-1} \)
B
\( \frac{\pi}{2} \text{ rad min}^{-1} \)
C
\( \pi \text{ rad min}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Angular speed is defined as the total angular displacement divided by the total time taken. The minute hand of a clock completes one full revolution in 60 minutes.
Formula:$$ \omega = \frac{2\pi}{T} $$
Solution:- One complete revolution is \( 2\pi \text{ radians} \).
- The time taken for one revolution of a minute hand is \( 60 \text{ minutes} \).
- Therefore, \( \omega = \frac{2\pi}{60} \text{ rad/min} \).
- Simplifying the fraction gives \( \frac{\pi}{30} \text{ rad min}^{-1} \).
Why other options are incorrect:- Option B assumes the hand completes a revolution in 4 minutes.
- Option C assumes the hand completes a revolution in 2 minutes.
#70 of 81
MDCAT 2017
Permalink
A body is moving in a circular path with constant speed. The magnitude of tangential and centripetal acceleration are:
A
\( \text{Tangential: } rv^2 \quad \text{Centripetal: } 0 \)
B
\( \text{Tangential: } 0 \quad \text{Centripetal: } \frac{v^2}{r} \)
C
\( \text{Tangential: } 0 \quad \text{Centripetal: } 0 \)
D
\( \text{Tangential: } \frac{v^2}{r} \quad \text{Centripetal: } \frac{v^2}{r} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:In uniform circular motion, speed is constant. Tangential acceleration measures the rate of change of
speed, while centripetal acceleration measures the rate of change of
direction.
Formula:$$ a_t = \frac{dv}{dt} \quad \text{and} \quad a_c = \frac{v^2}{r} $$
Solution:- Since speed \( v \) is perfectly constant, \( \Delta v = 0 \), meaning tangential acceleration \( a_t = 0 \).
- Because the body is traveling in a circle, its direction is continuously changing, which is driven by an inward centripetal acceleration of \( a_c = \frac{v^2}{r} \).
Why other options are incorrect:- Option C ignores the directional change required for circular motion.
- Option D wrongly assumes speed is changing.
#71 of 81
ETEA 2017
Permalink
A centripetal force F acts on a body moving with angular speed \( \omega \). If the angular speed is tripled, then the magnitude of centripetal force becomes:
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal force can be expressed in terms of angular velocity. The relationship reveals that the force scales with the square of the angular velocity.
Formula:$$ F_c = mr\omega^2 $$
Solution:- Let the initial force be \( F = mr\omega^2 \).
- If the new angular speed is \( \omega' = 3\omega \), substitute this into the formula.
- \( F' = mr(3\omega)^2 = mr(9\omega^2) = 9(mr\omega^2) \).
- Therefore, the new force is \( 9F \).
Why other options are incorrect:- Option C assumes force is directly proportional to \( \omega \), ignoring the square.
- Option A and Option D are mathematically incorrect for a factor of 3 squared.
#72 of 81
ETEA 2017
Permalink
A fly wheels rotates at a constant speed of \( 3000 \text{ rpm (rev/min)} \). The angle described by the shaft in radian in one second is:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:RPM (revolutions per minute) needs to be converted into radians per second to determine the angular displacement in one second.
Formula:$$ \omega = \frac{2\pi N}{60} $$
Solution:- Given \( N = 3000 \text{ rev/min} \).
- Convert revolutions to radians: \( 3000 \text{ rev} \times 2\pi = 6000\pi \text{ radians} \).
- Convert minutes to seconds by dividing by 60: \( \omega = \frac{6000\pi}{60} \).
- \( \omega = 100\pi \text{ radians per second} \).
- Since the time interval is 1 second, the angle described is \( 100\pi \text{ radians} \).
Why other options are incorrect:- Option A represents just one single revolution.
- Option B and Option D result from incorrect division or omitting the \( 2\pi \) conversion factor.
#73 of 81
ETEA 2016
Permalink
A wheel starts from rest and has an angular acceleration of \( 4.0 \text{ rad/s}^2 \). When it has made 10 rev its angular velocity is:
D
\( 250 \text{ rad/s} \)
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:To find the final angular velocity using angular acceleration and displacement, we use the third equation of rotational motion.
Formula:$$ \omega_f^2 = \omega_i^2 + 2\alpha\theta $$
Solution:- The wheel starts from rest, so \( \omega_i = 0 \).
- Convert revolutions to radians: \( \theta = 10 \text{ rev} \times 2\pi = 20\pi \text{ rad} \approx 62.83 \text{ rad} \).
- Plug in the values: \( \omega_f^2 = 0 + 2(4.0)(20\pi) = 160\pi \).
- \( 160 \times 3.1416 \approx 502.6 \).
- Take the square root: \( \omega_f = \sqrt{502.6} \approx 22.4 \text{ rad/s} \).
- The closest option is 22 rad/s.
Why other options are incorrect:- Option A, Option C, Option D occur if one forgets to multiply by \( 2\pi \) for radians or forgets to take the final square root.
#74 of 81
ETEA 2016
Permalink
A child riding on a large merry-go-round, travels a distance of \( 3000 \text{ m} \) in a circle of diameter \( 40 \text{ m} \). The total angle through which she revolves is:
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:The total angle revolved by an object is exactly equal to the total distance traveled along the arc divided by the radius of the circular path.
Formula:$$ \theta = \frac{S}{r} $$
Solution:- The diameter is \( 40 \text{ m} \), so the radius \( r \) is \( \frac{40}{2} = 20 \text{ m} \).
- The linear distance traveled \( S = 3000 \text{ m} \).
- Divide distance by radius: \( \theta = \frac{3000}{20} = 150 \text{ radians} \).
Why other options are incorrect:- Option B (75 rad) mistakenly uses the diameter (40m) instead of the radius in the denominator.
- Option A and Option D result from using incorrect formulas involving \( \pi \) unnecessarily.
#75 of 81
ETEA 2016
Permalink
The angular velocity for daily rotation of the earth is:
A
\( \frac{\pi}{3} \text{ radian hr}^{-1} \)
B
\( \frac{\pi}{6} \text{ radian hr}^{-1} \)
C
\( \frac{\pi}{12} \text{ radian hr}^{-1} \)
D
\( 12\pi \text{ radian hr}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option C
Diagnostic Explanation
Concept:Angular velocity represents the angle swept by an object per unit time. The Earth completes one full rotation on its axis every 24 hours.
Formula:$$ \omega = \frac{\Delta \theta}{\Delta t} $$
Solution:- One full rotation equals \( 2\pi \text{ radians} \).
- The time period \( T \) is 24 hours.
- Therefore, \( \omega = \frac{2\pi}{24 \text{ hr}} \).
- Simplify the fraction: \( \omega = \frac{\pi}{12} \text{ rad hr}^{-1} \).
Why other options are incorrect:- Option B assumes a 12-hour day.
- Option A assumes a 6-hour day.
- Option D incorrectly multiplies instead of dividing.
#76 of 81
ETEA 2013
Permalink
The centripetal acceleration of a car travelling at constant speed around a frictionless circular track:
B
Has constant magnitude but varying direction
C
Has constant direction but varying magnitude
D
Has varying magnitude and direction
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:Centripetal acceleration is a vector quantity. Even if an object's speed is constant, moving in a circle means its direction of motion is continuously changing, so the acceleration direction changes as well.
Formula:$$ |\vec{a}_c| = \frac{v^2}{r} $$
Solution:- Since speed \( v \) and radius \( r \) are constant, the magnitude of acceleration \( \frac{v^2}{r} \) remains perfectly constant.
- However, centripetal acceleration always points toward the center. As the car moves along the track, the absolute spatial direction of 'toward the center' continuously rotates.
- Therefore, it has a constant magnitude but varying direction.
Why other options are incorrect:- Option A is wrong because circular motion requires acceleration to change the velocity vector's direction.
- Option C is mathematically impossible for circular motion.
- Option D is incorrect because the magnitude remains constant.
#77 of 81
MDCAT 2011
Permalink
Radian is a unit of angular displacement which can also be measured in degrees. How many radians are equal to one degree?
View Answer & Propolis Autopsy
Correct Key: Option B
Diagnostic Explanation
Concept:A full circle consists of \( 360^\circ \), which is equivalent to \( 2\pi \) radians.
Formula:$$ 360^\circ = 2\pi \text{ rad} $$
Solution:- Start with the standard equivalence: \( 180^\circ = \pi \text{ radians} \).
- Divide both sides by 180 to isolate one degree.
- \( 1^\circ = \frac{\pi}{180} \text{ radians} \).
Why other options are incorrect:- Option A is the inverted conversion factor (used to convert radians to degrees).
- Option C would simplify to \( \frac{\pi}{90} \), which is \( 2^\circ \).
- Option D confuses the numerical value of 1 radian (\( 57.3^\circ \)) with the fraction layout.
#78 of 81
MDCAT 2010
Permalink
A wheel of radius \( 1 \text{ m} \) covers an angular displacement of \( 180^\circ \). Its linear displacement is:
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Linear displacement (arc length) relates to angular displacement, but the angle must first be converted from degrees into radians.
Formula:$$ S = r\theta $$
Solution:- Convert \( 180^\circ \) to radians: \( 180^\circ = \pi \text{ radians} \).
- Given radius \( r = 1 \text{ m} \).
- Calculate the arc length: \( S = (1 \text{ m})(\pi \text{ rad}) = \pi \text{ m} \).
- Since \( \pi \approx 3.14 \), the linear displacement is \( 3.14 \text{ m} \).
Why other options are incorrect:- Option B incorrectly uses \( 360^\circ \) or \( 2\pi \).
- Option C is a unit of angle, not a unit of linear distance.
- Option D is a calculation error involving improper conversion factors.
#79 of 81
ETEA 2010
Permalink
When a body moves in a circle the angle between its linear velocity and angular velocity is always:
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:In uniform circular motion, the linear velocity vector lies tangent to the circular path, while the angular velocity vector points along the axis of rotation.
Formula:$$ \vec{v} = \vec{\omega} \times \vec{r} $$
Solution:- By the right-hand rule, \( \vec{\omega} \) is perpendicular to the entire plane of motion.
- Since \( \vec{v} \) is strictly in the plane of motion, the angle between the plane and its normal axis is exactly \( 90^\circ \).
Why other options are incorrect:- Option A and Option B imply they are parallel or anti-parallel, which violates the cross-product vector definition.
- Option C is geometrically equivalent to \( 0^\circ \).
#80 of 81
MDCAT 2009
Permalink
Linear velocity or tangential velocity of any particle moving in a circular path of radius \( 2 \text{ m} \) with angular velocity \( 8 \text{ rad s}^{-1} \) will be:
A
\( 16 \text{ ms}^{-1} \)
B
\( 10 \text{ ms}^{-1} \)
C
\( 4 \text{ ms}^{-1} \)
D
\( 6 \text{ ms}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option A
Diagnostic Explanation
Concept:Linear (tangential) velocity is directly proportional to both the angular velocity of the object and the radius of its circular path.
Formula:$$ v = r\omega $$
Solution:- Given radius \( r = 2 \text{ m} \).
- Given angular velocity \( \omega = 8 \text{ rad s}^{-1} \).
- Multiply the two: \( v = 2 \times 8 = 16 \text{ ms}^{-1} \).
Why other options are incorrect:- Option B, Option C, Option D result from incorrect arithmetic operations (like addition, subtraction, or division instead of multiplication).
#81 of 81
MDCAT 2008
Permalink
The force required to bend the normally straight path of a particle into a circular path is called ____ force.
View Answer & Propolis Autopsy
Correct Key: Option D
Diagnostic Explanation
Concept:By Newton's first law, an object will move in a straight line unless acted upon by an external force. To continuously 'bend' this path into a circle, a force must constantly pull the object toward the center of rotation.
Formula:$$ F_c = \frac{mv^2}{r} $$
Solution:- The center-seeking force responsible for maintaining circular motion is defined universally as centripetal force.
Why other options are incorrect:- Centrifugal force is an outward-directed pseudo-force observed in rotating reference frames, not the force bending the path.
- Traveling and Bending are not standard physical forces.
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