Physics
120 Solved Past Papers
2005 – 2024 Archives
Force & Motion Past Papers
Solved past paper MCQs for Force & Motion from official UHS, NUMS, SZABMU, DUHS, and KMU examinations. Includes verified distractor autopsies and step-by-step cognitive explanations.
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The quantity of motion present in a body can be measured by ____. [SZABMU 2024]
A
Acceleration
B
Momentum
C
Speed
D
Velocity
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Historical definitions of physical quantities by Isaac Newton.
Solution:
Newton originally coined the phrase "quantity of motion" to describe how hard it is to stop a moving object.
Because stopping power depends heavily on both the object's mass and its velocity, the exact physical measure is momentum (\( \vec{P} = m\vec{v} \)).
Why other options are incorrect:
Velocity and speed describe how fast it moves, but completely ignore the mass. A speeding bullet and a speeding train have the same speed, but vastly different "quantities of motion" (momentum).
The slope of velocity-time graph gradually decreases, then the body is said to be moving with [SZABMU 2024]
A
Negative acceleration
B
Positive acceleration
C
Uniform velocity
D
Variable acceleration
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The slope of a velocity-time graph is identically the acceleration.
Solution:
If the slope is "gradually decreasing," it means the value of the slope is changing at every point.
Because slope = acceleration, a changing slope strictly dictates a changing, non-constant acceleration.
Therefore, the body is moving with variable acceleration.
Why other options are incorrect:
"Negative acceleration" just tells you the sign of a constant slope. "Uniform velocity" would mean zero acceleration. Only "Variable" directly captures the changing nature of the slope.
The acceleration can be determined by the gradient of ____ [SZABMU 2024]
A
Displacement-time graph
B
Force-time graph
C
Speed-time graph
D
Velocity-time graph
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Definition of acceleration through kinematics.
Solution:
Acceleration is the rate of change of the velocity vector over time (\( \vec{a} = \frac{\Delta \vec{v}}{\Delta t} \)).
The gradient (slope) of a velocity-time graph mathematically plots this exact \( \frac{\Delta y}{\Delta x} \) ratio.
Why other options are incorrect:
Displacement-time gives velocity. Speed-time gives magnitude of acceleration but lacks the crucial directional vector data required for true acceleration.
The two-dimensional motion under constant acceleration due to gravity is called: [UHS 2024]
A
Circular motion
B
Rotational motion
C
Projectile motion
D
Vibratory motion
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Standard definition of classical kinematic trajectories.
Solution:
When an object is launched into a 2D plane (x and y axes) and the only significant force acting on it is the constant downward pull of gravity, it traces a parabolic path.
This specific physical scenario is formally titled "Projectile Motion".
Why other options are incorrect:
Circular motion requires a centripetal force constantly changing direction. Vibratory motion is 1D oscillation. Rotational deals with spinning objects.
If you stops your car quickly by wearing seat belts, chance of injury is greatly reduced because seat belt applied [NUMS 2024]
A
Extra force
B
Perpendicular force
C
Opposite force
D
Zero force
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Seatbelts utilize the impulse-momentum theorem and Newton's Third Law to protect passengers.
Solution:
During a sudden stop, your body wants to continue forward due to inertia.
The seatbelt stretches slightly, applying a restraining force directly backward (opposite) against your chest to safely reduce your momentum over a longer time span.
This opposite force counters the forward inertia, preventing a high-force impact with the windshield.
Why other options are incorrect:
Extra force is vague. Perpendicular force would push you sideways. Zero force means the seatbelt did absolutely nothing to restrain you.
Electric Flux is the dot product of Electric field (vector) and Area (vector), resulting in a pure scalar.
Work Done is the dot product of Force (vector) and Displacement (vector), also resulting in a scalar.
All forms of Energy (including Potential) are scalar quantities by definition.
Since none of the options require a spatial direction to be fully defined, "None of the given options" is correct.
Why other options are incorrect:
Students mistakenly associate "electric" or "work" with vectors because their component formulas contain vectors, but dot products always yield scalars.
Which of the following believed in absolute time? [BUMHS 2024]
I Newton II Galileo
A
I
B
II
C
Both I and II
D
Neither I nor II
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Historical paradigm of classical mechanics before Einstein's relativity.
Solution:
Both Galileo Galilei and Isaac Newton constructed their entire frameworks of classical kinematics upon the rigid assumption that time is a universal, absolute constant.
In their universe, one second ticking on Earth was mathematically identical to one second ticking anywhere else, perfectly independent of an observer's speed or gravity.
It wasn't until Albert Einstein's Special Relativity that time was proven to be relative.
Why other options are incorrect:
Selecting only one ignores that classical mechanics as a whole was founded on absolute time.
A 40kg body starting from rest falls through a vertical distance of 125cm to ground. The velocity of the body just before it hits the ground is: [BUMHS 2024]
A
\( 250 \text{ m/s} \)
B
\( (250) \text{ m/s} \)
C
\( 25 \text{ m/s} \)
D
\( 5 \text{ m/s} \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Energy conservation or the third equation of kinematics, heavily relying on strict unit conversion.
Formula:
$$ v = \sqrt{2gh} $$
Solution:
Mass is irrelevant for free fall speed.
CRITICAL: Convert height from cm to meters. \( h = 125 \text{ cm} = 1.25 \text{ meters} \).
Use gravity \( g = 10 \text{ m/s}^2 \) (standard estimation).
$$ v = \sqrt{2 \times 10 \times 1.25} $$
$$ v = \sqrt{25} = 5 \text{ m/s} $$
Why other options are incorrect:
If a student forgets to convert cm to meters, they calculate \( \sqrt{2 \times 10 \times 125} = \sqrt{2500} = 50 \). If they didn't square root properly, they might land on 25. The 40kg mass is purely a distractor.
A person's life was saved in a car accident due to airbags system. During that car accident, airbags expanded in front of head of that person. If that car was not equipped with airbags then movement of head would be stopped by windshield in much faster time. Airbags saved life because it [BUMHS 2024]
A
causes much greater force for longer time
B
causes much greater force for smaller time
C
causes much smaller force for longer time
D
causes much smaller force for smaller time
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Impulse-Momentum Theorem applications to human safety.
Formula:
$$ F = \frac{\Delta p}{\Delta t} $$
Solution:
In a crash, the passenger's momentum must be reduced to strictly zero (\( \Delta p \) is fixed).
Airbags are soft, meaning they gently compress as the head hits them. This dramatically stretches out the impact time interval (\( \Delta t \) increases).
Because time is in the denominator, a much larger time mathematically produces a much smaller impact force on the skull.
Why other options are incorrect:
Greater force would shatter the skull. Smaller time (hitting the hard glass) mathematically spikes the force to lethal levels.
Which of the following statements is absolutely correct:- [BUMHS 2024]
I. Forces can stop or make objects move faster II. Forces can change the direction of movement
A
I
B
II
C
Both I and II
D
Neither I nor II
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The foundational capabilities of force as defined by Newton.
Solution:
A net external force produces an acceleration vector.
If this acceleration acts against motion, the object slows/stops (Statement I).
If it acts with motion, it speeds up (Statement I).
If the force acts perpendicular or diagonally to the current velocity (like gravity on a projectile or a steering wheel turning a car), it alters the path/direction (Statement II).
Therefore, both statements flawlessly describe classical force mechanics.
Why other options are incorrect:
Excluding either statement artificially ignores half of Newton's Second Law.
Distinguishing between inertial mass and gravitational mass formulas.
Solution:
Gravitational mass measures an object's precise response to a gravitational field, dictating its weight.
The weight formula is \( W = m_gg \).
Rearranging for gravitational mass gives \( m_g = \frac{W}{g} \).
Why other options are incorrect:
\( F/a \) calculates strictly inertial mass (resistance to general acceleration). While experimentally equivalent to gravitational mass, its formulaic definition arises from Newton's Second Law, not gravitation.
A set of coordinate axes in which measurements are made is called: [BUMHS 2024]
A
Cartesian coordinates
B
Rectangular coordinates
C
Spherical coordinates
D
Frame of reference
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The overarching physical terminology for an observation platform.
Solution:
In physics, you cannot measure position or velocity in a vacuum; you must attach your ruler and clock to a specific, defined viewpoint.
A coordinate system (like x, y, z axes) combined with a synchronized clock constitutes a "Frame of Reference".
It is the foundational stage upon which all kinematic measurements are mathematically evaluated.
Why other options are incorrect:
Cartesian, rectangular, and spherical describe specific mathematical geometry types of coordinates, but the physical concept defining the measurement space itself is strictly the Frame of Reference.
Which of the following is the correct definition of variable velocity? [UHS 2023]
A
Unequal distances are covered in equal intervals of time
B
Equal displacements are made in unequal intervals of time
C
Unequal displacements are made in equal intervals of time
D
Equal displacements are made in equal intervals of time
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Velocity defines the strict rate of change of displacement over time.
Solution:
If a body has uniform velocity, it covers the exact same displacement (same distance, same direction) every single second.
Variable velocity occurs if the rate changes. Thus, measuring equal time intervals (e.g., 1-second chunks) will yield unequal displacement vectors (either a different distance was covered, or it turned a corner).
Why other options are incorrect:
Option A describes variable speed (because distance is scalar). Option D describes uniform velocity.
The velocity-time plot for a moving particle shows a straight line. This means: [UHS 2023]
A
The particle has constant acceleration
B
The particle has never turned around
C
The particle has zero displacement
D
The data in insufficient
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The slope of a velocity-time graph represents acceleration.
Solution:
A straight line strictly possesses a constant, unchanging geometric slope.
Because the slope is constant, the physical quantity it represents (acceleration) must also be perfectly constant.
It might be zero (horizontal line) or a non-zero constant (tilted line), but it strictly classifies as uniform/constant acceleration.
Why other options are incorrect:
If the line crosses the x-axis, the velocity becomes negative, meaning the particle DID turn around. Displacement is the area under the curve, which changes constantly.
A net resultant force is strictly required to produce an acceleration (Newton's Second Law). Acceleration occurs if either speed OR direction changes.
Solution:
A car moving around a bend is constantly changing its direction of travel.
Because velocity is a vector, this continuous change in direction constitutes an acceleration, even if the speedometer (speed) remains constant.
To create this centripetal acceleration, a resultant force (friction from the tires) must be acting toward the center of the bend.
Why other options are incorrect:
Stationary cars, or cars moving straight ahead at constant velocity (horizontal or uphill), have strictly zero acceleration. Thus, their resultant net force is zero.
Momentum is product of mass and velocity, then momentum and velocity are: [SZABMU 2023]
A
Parallel
B
Perpendicular
C
Antiparallel
D
Independent
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Multiplying a vector by a strictly positive scalar preserves its direction entirely.
Formula:
$$ \vec{p} = m\vec{v} $$
Solution:
Mass (\( m \)) is an intrinsically positive scalar quantity.
When the velocity vector (\( \vec{v} \)) is multiplied by mass, the resulting momentum vector (\( \vec{p} \)) is scaled up, but its geometric direction is untouched.
Therefore, momentum ALWAYS points exactly in the same direction as velocity. Vectors in the same direction are parallel.
Why other options are incorrect:
Antiparallel would require a negative mass, which does not exist in classical physics.
A body is moved through a displacement of 15m towards North, the total displacement will be zero when body covered the same displacement towards: [ETEA 2023]
A
North
B
South
C
West
D
East
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Displacement vectors sum geometrically. To achieve a net zero displacement, the return vector must perfectly cancel the initial vector.
Solution:
Initial vector: \( +15 \text{ m} \) North.
To return to the exact starting point (origin), the body must travel precisely backward along the same line.
The opposite compass direction of North is South. Covering 15m South perfectly zeroes the displacement.
Why other options are incorrect:
More North simply adds distance. East and West create diagonal hypotenuse displacements (Pythagorean theorem).
Doubling the initial velocity of a projectile while keeping all other parameters the same, the height reached by the projectile increases by: [ETEA 2023]
A
Two times
B
Three times
C
Four times
D
Remains the same
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The maximum height of a projectile is proportional to the square of its initial velocity.
Formula:
$$ H = \frac{v_i^2 \sin^2\theta}{2g} $$
Solution:
Height \( H \) varies directly with \( v_i^2 \).
If \( v_i \) is replaced by \( (2v_i) \), then: $$ H_{new} \propto (2v_i)^2 = 4v_i^2 $$
Thus, \( H_{new} = 4H \). The height strictly increases by a factor of four.
Why other options are incorrect:
Assuming a linear relationship (ignoring the square) would wrongly suggest it increases by two times.
Neglecting the effect of air resistance how long a stone takes to dropped of a 125 m high building lands on the ground, take g = \( 10 \text{ m/s}^2 \): [ETEA 2023]
A
3 sec
B
4 sec
C
18 sec
D
5 sec
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The time taken for an object dropped from rest to hit the ground strictly depends on the height and gravity.
Formula:
$$ S = v_it + \frac{1}{2}gt^2 $$
Solution:
Because it is dropped, initial velocity \( v_i = 0 \).
Take the square root: \( t = 5 \text{ seconds} \).
Why other options are incorrect:
Failing to take the square root results in 25. Ignoring the \( 1/2 \) multiplier gives roughly 3.5s. Simple arithmetic errors lead to the other values.
What will be the value of acceleration, if a body of mass 0.5 Kg is acted upon by a force of 10 N? [SINDH 2023]
A
40 m/s²
B
5 m/s²
C
10 m/s²
D
20 m/s²
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Newton's Second Law directly relates force, mass, and acceleration.
Formula:
$$ F = ma \implies a = \frac{F}{m} $$
Solution:
Force \( F = 10 \text{ N} \).
Mass \( m = 0.5 \text{ kg} \).
Substitute values: $$ a = \frac{10}{0.5} $$
$$ a = 20 \text{ m/s}^2 $$
Note: The options provided in the source use 'N' as the unit, which is a typographical error in the original paper (it should be \( \text{m/s}^2 \)). We select 20 based on the numerical value.
Why other options are incorrect:
Multiplying 10 by 0.5 yields 5. Mathematical errors in division yield 40 or 10.
Due to sudden rain, which of the following is true for the car moving on the road? [SINDH 2023]
A
Force of engine decreases
B
Balance will not be maintained
C
Direction of motion will be effected
D
Linear momentum increases
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Friction is heavily dependent on the nature of the surfaces in contact. Water acts as a lubricant.
Solution:
Rain introduces water between the car's tires and the asphalt, significantly reducing the coefficient of friction.
Without sufficient friction, the tires lose their grip, causing the car to slide (hydroplane) and lose its steady balance and control.
Why other options are incorrect:
Rain does not directly decrease the engine's mechanical power. Direction isn't necessarily affected unless a turn is attempted. Momentum does not suddenly increase just because the road is wet.
Two bodies of mass 10 kg and 40 kg are dropped from the same height at the same time. Value of which to the following remains the same during the motion of the two bodies? [SINDH 2023]
A
Acceleration
B
Kinetic energy
C
Potential energy
D
Power
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
In the absence of air resistance, all bodies strictly fall at the identical rate of acceleration regardless of their mass.
Solution:
Galileo famously demonstrated that acceleration due to gravity (\( g \approx 9.8 \text{ m/s}^2 \)) is entirely independent of an object's mass.
Therefore, both the 10kg and 40kg bodies experience the exact same uniform downward acceleration.
Why other options are incorrect:
Kinetic and potential energies strictly depend on mass (\( \frac{1}{2}mv^2 \) and \( mgh \)). Since their masses are different, their energies are vastly different. Power also depends on mass.
A force 2F acting on a particle of mass 10kg produces an acceleration of \( 30 \text{ m/s}^2 \). a force 5F acting on a particle of mass M, produces an acceleration of \( 25 \text{ m/s}^2 \). What is the mass? [SINDH 2023]
A
30 kg
B
21 kg
C
4.8 kg
D
3.3 kg
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Use Newton's Second Law sequentially to link the two scenarios.
Formula:
$$ F_{net} = ma $$
Solution:
Scenario 1: $$ 2F = 10 \times 30 = 300 $$
This implies \( F = 150 \text{ N} \).
Scenario 2: A force of 5F acts on mass M. Force applied = \( 5 \times 150 = 750 \text{ N} \).
Set up equation 2: $$ 750 = M \times 25 $$
Solve for M: $$ M = \frac{750}{25} = 30 \text{ kg} $$
Why other options are incorrect:
Algebraic errors solving for F or dividing incorrectly result in the other distractor values.
The rate of change of displacement with respect to time is the direct physical definition of velocity.
Why other options are incorrect:
Acceleration is the slope of velocity-time. Distance is the magnitude of a purely scalar path length. Displacement is read directly from the y-axis itself.
The gradient of velocity time is equal to: [SZABMU 2022]
A
Distance
B
Force
C
Acceleration
D
Speed
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The mathematical gradient (or slope) of a line on a Cartesian plane is the ratio of the change in the y-axis variable to the change in the x-axis variable.
In a velocity-time graph, the y-axis represents velocity (\( v \)) and the x-axis represents time (\( t \)).
The rate of change of velocity with respect to time (\( \frac{\Delta v}{\Delta t} \)) is the direct definition of acceleration.
Why other options are incorrect:
The area under the graph gives displacement/distance. Force requires mass (Newton's 2nd Law). Speed is a scalar magnitude of velocity, not its gradient over time.
Because only angles that satisfy the trigonometric identity \( \sin(2(90^\circ-\theta)) = \sin(180^\circ-2\theta) = \sin(2\theta) \) will yield the same range.
Two cars travelling on straight road in opposite direction with speed \( 70 \text{ kmh}^{-1} \) and \( 60 \text{ kmh}^{-1} \), their relative velocity will be: [SZABMU 2022]
A
\( 10 \text{ kmh}^{-1} \)
B
\( 130 \text{ kmh}^{-1} \)
C
\( 65 \text{ kmh}^{-1} \)
D
\( 5 \text{ kmh}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Relative velocity measures how fast one object is moving from the perspective of another. When objects move in opposite directions, their approach (or separation) rate is the sum of their individual speeds.
Formula:
$$ \vec{v}_{rel} = \vec{v}_1 - \vec{v}_2 $$
Solution:
Let the first car's velocity be \( \vec{v}_1 = +70 \text{ km/h} \).
Since the second car moves in the opposite direction, \( \vec{v}_2 = -60 \text{ km/h} \).
The relative velocity magnitude is \( |\vec{v}_{rel}| = |70 - (-60)| = 130 \text{ km/h} \).
Why other options are incorrect:
Subtracting the magnitudes (10 km/h) applies only if they are travelling in the same direction. Averaging them (65 km/h) has no physical meaning here.
Substitute this into the equation for the first body: $$ v_1' = \left( \frac{m - m}{m + m} \right)v_1 + \left( \frac{2m}{2m} \right)v_2 = (0)v_1 + (1)v_2 = v_2 $$
Similarly, for the second body, \( v_2' = v_1 \).
Therefore, they simply swap velocities.
Why other options are incorrect:
Options A and B represent a specific subset where one of the bodies is initially at rest. Option C suggests they bounce back with their own reversed velocities, which only happens if they hit a massive immovable wall.
Slope of distance time graph can never be: [SZABMU 2022]
A
Positive
B
Negative
C
Constant
D
Zero
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Distance is a scalar quantity that measures the total length of the path covered by a moving object. Because it is a cumulative total, it can only increase or remain the same.
Solution:
The slope of a distance-time graph represents speed (\( \frac{\Delta d}{\Delta t} \)).
Since distance cannot physically decrease over time, \( \Delta d \) must always be greater than or equal to zero.
Therefore, the slope can be positive (moving) or zero (stationary), but it can mathematically and physically never be negative.
Why other options are incorrect:
Displacement-time graphs CAN have a negative slope (if returning toward the origin), but distance is fundamentally additive.
Projectile motion combines uniform horizontal motion and uniformly accelerated vertical motion due to gravity.
Solution:
Throughout the entire flight, the horizontal velocity \( v_x \) remains constant because there is no horizontal force (ignoring air resistance).
The vertical velocity \( v_y \) decreases as the object rises, reaching exactly zero at the absolute highest point of the trajectory, before becoming negative as it falls back down.
Therefore, at the peak, \( v_y = 0 \) and \( v_x = \text{constant} \).
Why other options are incorrect:
If \( v_x \) was also zero (Option A), the projectile would drop straight down like a stone. Gravity ensures \( v_y \) is never constant (Option C, D).
A body covers displacement of 10m towards North and returns back to initial point by covering 10m towards south, its total displacement is: [ETEA 2022]
A
20m North
B
10m South
C
0m along North-south
D
0m
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Displacement is a vector quantity defined strictly as the shortest straight-line distance between the final position and the initial position.
In Newton's first law of motion which quantity remains constant: [ETEA 2022]
A
Velocity
B
Angular displacement
C
Amplitude
D
Amount of work
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Newton's First Law (Law of Inertia) states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force.
Solution:
"Uniform motion in a straight line" is the exact definition of constant velocity.
If the net force is zero, the acceleration is zero.
Zero acceleration strictly means the velocity vector (both magnitude and direction) remains absolutely constant.
Why other options are incorrect:
Angular displacement, amplitude, and work are not the fundamental quantities preserved by translational inertia. An object can have constant velocity while its displacement continuously changes.
The Law of Inertia (Newton's First Law) applies exclusively when the net external force on a system is strictly zero.
Solution:
When the sum of all forces acting on an object is zero (\( \Sigma F = 0 \)), the object is in a state of translational equilibrium.
Because the law of inertia describes motion precisely under this \( \Sigma F = 0 \) condition, it inherently satisfies the first condition of equilibrium.
Why other options are incorrect:
Variable forces or contact forces induce acceleration, violating the premise of inertia. Mass conservation is a separate principle altogether.
A projectile is launched, its velocity is maximum at: [ETEA 2022]
A
Point of projection
B
Highest point
C
Between launching and highest point
D
All points
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The total velocity of a projectile is the vector sum of its horizontal and vertical components. As it rises against gravity, its kinetic energy decreases and converts to potential energy.
Solution:
At the point of projection, the projectile possesses its full initial vertical velocity (\( v_{iy} \)) and horizontal velocity (\( v_x \)).
As it moves upward, \( v_x \) remains constant, but \( v_y \) strictly decreases, meaning the overall magnitude \( v = \sqrt{v_x^2 + v_y^2} \) decreases.
The velocity is at its absolute minimum at the highest point (where \( v_y = 0 \)). It returns to its maximum magnitude right as it hits the ground (landing point). Assuming a ground-to-ground launch, projection and landing share the maximum speed.
Why other options are incorrect:
The highest point has the minimum velocity. Velocity is not constant across all points.
Dividing the total net displacement covered during an entire journey by the total elapsed time yields a single summarizing value.
This macro-level calculation is the formal definition of average velocity.
Why other options are incorrect:
Instantaneous velocity is measured at a precise moment (\( \Delta t \to 0 \)). Uniform and variable velocities are states of motion, not defined merely by a bulk division formula.
The velocity time graph of a motion starting from rest with uniform acceleration is a straight line: [ETEA 2022]
A
Not passing through origin
B
Parallel to time axis
C
Parallel to velocity axis
D
Passing through origin
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
A velocity-time graph maps velocity on the y-axis against time on the x-axis. The slope of this graph is the acceleration.
Formula:
$$ v = v_i + at $$
Solution:
The object starts from rest, meaning initial velocity \( v_i = 0 \).
Substituting this gives the equation \( v = at \).
This is a linear equation matching the form \( y = mx + c \), where \( c = 0 \) (the y-intercept).
Because the y-intercept is exactly 0, the straight line must strictly pass through the origin (0,0).
Why other options are incorrect:
If it did not pass through the origin, \( v_i \) would not be zero. Parallel to time axis means zero acceleration. Parallel to velocity axis is physically impossible.
A projectile is thrown at an angle of \( 45^\circ \) with horizontal and its range is \( R_1 \). Another projectile is thrown at an angle of \( 45^\circ \) with vertical and its range is \( R_2 \). The relation between \( R_1 \) and \( R_2 \) is: [ETEA 2022]
A
\( R_2 = 2R_1 \)
B
\( R_1 = 2R_2 \)
C
\( R_1 = R_2 \)
D
\( 3R_1 = R_2 \)
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Standard kinematics uses the angle relative to the horizontal to calculate range.
Solution:
Projectile 1: Angle with horizontal is \( \theta_1 = 45^\circ \).
Projectile 2: Angle with the vertical is \( 45^\circ \). Because the axes are orthogonal (\( 90^\circ \)), the angle with the horizontal is \( 90^\circ - 45^\circ = 45^\circ \). So, \( \theta_2 = 45^\circ \).
Since both projectiles are effectively launched at the exact same horizontal angle (\( 45^\circ \)), assuming equal initial velocities, their ranges will be absolutely identical.
Therefore, \( R_1 = R_2 \).
Why other options are incorrect:
Any factor scaling implies the angles resulted in different trigonometric outputs, which is false here.
4.9 comes from dividing by 2 (confusing with distance formula). 9.4 is a typo for 9.8 (1 second of fall). The decimal point shifts represent basic calculation errors.
A box of mass m = 6kg slides with speed v = 4m/s across a frictionless floor, it suddenly explodes into two pieces. One piece, with mass \( m_1 \) = 2kg moves in the same direction with speed \( v_1 \)=8 m/s. The velocity of the second piece is: [DUHS 2022]
A
6 m/sec
B
3 m/sec
C
1 m/sec
D
4 m/sec
E
2 m/sec
View Answer & Propolis Autopsy
Correct Key: Option EDiagnostic Explanation
Concept:
An explosion is governed by internal forces. Therefore, the total momentum of the isolated system is perfectly conserved before and after the explosion.
Formula:
$$ P_{initial} = P_{final} $$
$$ mv = m_1v_1 + m_2v_2 $$
Solution:
Total initial momentum: \( 6 \text{ kg} \times 4 \text{ m/s} = 24 \text{ kg m/s} \).
After explosion, Piece 1 mass \( m_1 = 2 \text{ kg} \) and \( v_1 = 8 \text{ m/s} \). Its momentum = \( 2 \times 8 = 16 \text{ kg m/s} \).
A helicopter of weight 'W' is ascending with zero acceleration. The upward force 'F' on it is: [DUHS 2022]
A
\( F > W \)
B
\( F = \sqrt{W} \)
C
\( F = 0 \)
D
\( F = W \)
E
\( F < W \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
According to Newton's Second Law, acceleration is directly proportional to net force. Zero acceleration implies zero net force.
Formula:
$$ \Sigma F = ma $$
$$ F_{up} - F_{down} = m(0) $$
Solution:
The upward force is the lift \( F \).
The downward force is the weight \( W \).
Since acceleration is exactly zero (it is moving at a steady, uniform velocity), the forces must perfectly balance.
$$ F - W = 0 \implies F = W $$
Why other options are incorrect:
If \( F > W \), the helicopter would be accelerating upward (speeding up). If \( F < W \), it would be decelerating (slowing down). Zero force implies no lift, meaning it would be in freefall.
When a body moves with uniform velocity than it's: [DUHS 2022]
A
Average velocity is zero
B
Instantaneous velocity is greater than average velocity
C
Instantaneous velocity is zero
D
Instantaneous velocity is equal to average velocity
E
Instantaneous velocity is less than average velocity
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Uniform velocity means the object's speed and direction remain absolutely constant for the entire duration of motion.
Solution:
If a car drives strictly at \( 60 \text{ km/h} \) East without ever speeding up, slowing down, or turning, its velocity at any given split-second (instantaneous) is \( 60 \text{ km/h} \) East.
If you calculate the total displacement over total time (average), it will also perfectly yield \( 60 \text{ km/h} \) East.
Therefore, for uniform motion, the instantaneous velocity is permanently identical to the average velocity.
Why other options are incorrect:
Differences between average and instantaneous only arise if the velocity fluctuates (acceleration/deceleration) over the journey.
An elastic collision is the one in which: [NUMS 2022]
A
Kinetic energy and momentum is conserved
B
Kinetic is conserved but total energy is not conserved
C
Momentum is conserved but kinetic energy is not conserved
D
Both kinetic energy and momentum are not conserved
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Collisions in isolated systems always conserve linear momentum. How they handle kinetic energy dictates their specific classification.
Solution:
By universal law, total momentum is conserved in all types of collisions.
An "elastic" collision is strictly defined as a perfect bounce where absolutely zero macroscopic kinetic energy is converted into heat, sound, or permanent deformation.
Therefore, both kinetic energy and momentum remain exactly equal before and after the impact.
Why other options are incorrect:
Option C defines an inelastic collision. Option B violates the fundamental First Law of Thermodynamics (total energy is always conserved universally). Option D violates basic momentum conservation.
At 90 degrees, the projectile shoots straight up and lands at the start (Range = 0). 30 and 60 degrees provide equal ranges, but they are smaller than the peak range at 45 degrees.
Newton's Third Law governs action and reaction force pairs.
Solution:
Forces can mathematically cancel each other out ONLY if they are applied to the exact same object.
Newton's Third Law pairs (Action/Reaction) ALWAYS strictly apply to two different interacting bodies (A pushes B, B pushes A).
Because they act on different bodies, they dictate the respective motion of those different bodies independently. They can never cancel each other. Therefore, Option D is a false statement.
Why other options are incorrect:
Options A, B, and C are entirely true properties of Newton's Third Law.
Two busses moving at 100 km/h and 80 km/h respectively cross each other while moving in opposite direction. Velocity of one bus relative to other bus is: [NUMS 2022]
A
100 km/h
B
20 km/h
C
80 km/h
D
180 km/h
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
When two objects move in directly opposing directions, the speed at which the gap between them closes is the arithmetic sum of their respective speeds.
Formula:
$$ \vec{v}_{rel} = \vec{v}_1 - \vec{v}_2 $$
Solution:
Assign a directional axis. Let Bus 1 move forward: \( \vec{v}_1 = +100 \text{ km/h} \).
The explosion of explosive material is application of: [NUMS 2022]
A
Law of conservation of energy
B
Law of conservation of mass
C
Law of conservation of momentum
D
Newton's third law of motion
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
An explosion is a dramatic event driven entirely by internal forces within a closed system.
Solution:
Because no external forces act on the bomb at the exact instant of explosion, the total vector momentum of the system must remain constant.
A stationary bomb (zero momentum) will explode into fragments that fly off in all directions. The vector sum of all fragment momentums mathematically cancels out to exactly zero.
This makes explosions a classic demonstration of the Law of Conservation of Linear Momentum.
Why other options are incorrect:
Kinetic energy massively increases during an explosion (converting chemical potential to kinetic), making "energy conservation" a tricky descriptor for kinematic modeling here. Third law applies to specific pair fragments, but momentum conservation governs the entire system.
If two objects of equal masses 'm' are moving towards each other with the same speeds 'v' then what will be the total final momentum after elastic head-on collision? [MDCAT 2019]
A
\( -mv \text{ kg/s} \)
B
\( 2 mv \text{ kg/s} \)
C
\( mv \text{ kg m/s} \)
D
\( 0 \text{ kg m/s} \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Conservation of vector momentum.
Solution:
Total initial \( P = mv - mv = 0 \). Thus final is 0.
The range of the projectile depends upon the velocity of the projection and the angle of the projection i.e \( 45^\circ \). For a fixed velocity, when the angle of projection is larger than \( 45^\circ \). Which of the following is correct? [MDCAT 2019]
A
Both the height and the range attained by the projectile will be less
B
The height attained by the projectile will be less but the range is more
C
Both the height and the range attained by the projectile will be more
D
The height attained by the projectile will be more but the range is less
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Steeper angles increase vertical velocity but decrease efficiency of horizontal range past \( 45^\circ \).
Solution:
Height increases, Range decreases.
Why other options are incorrect:
Trigonometric fact of \( \sin^2\theta \) vs \( \sin(2\theta) \).
A cyclist is traveling at \( 15 \text{ ms}^{-1} \) she applies brakes so that she doesn't collide with the wall in front of her distance of 18m. Calculate the magnitude of deceleration. [MDCAT 2018]
A bullet of mass m moving with a velocity v is fired into large wooden block of mass M if the bullet remains embedded in the wooden block, the velocity of the system will be: [ETEA 2017]
A projectile is launched at \( 45^\circ \) to the horizontal with initial K, Energy, E. Assuming air resistance to be negligible, what will be the kinetic energy of the projectile when it reaches its highest point? [ETEA 2014]
A
\( 0.71 E \)
B
\( 0.50 E \)
C
\( 0.87 E \)
D
\( E \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
At max height, only horizontal velocity \( v_x = v_i \cos\theta \) exists.
Solution:
$$ K.E_{\text{top}} = \frac{1}{2}m(v_i \cos 45^\circ)^2 = E \cos^2(45^\circ) $$
$$ \cos^2(45^\circ) = 0.5 $$
So, \( K.E = 0.50 E \).
Why other options are incorrect:
0.71 E comes from forgetting to square the cosine.
One ball is thrown vertically upward with a velocity of 98 m/s. If the takes 10 seconds to reach the highest point, then the acceleration of the ball is [ETEA 2011]
A
\( 9.8 \text{ ms}^{-2} \)
B
\( 980 \text{ ms}^{-2} \)
C
\( 98 \text{ ms}^{-2} \)
D
\( -9.8 \text{ ms}^{-2} \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Acceleration opposes upward velocity.
Solution:
$$ a = \frac{0 - 98}{10} = -9.8 \text{ m/s}^2 $$
Why other options are incorrect:
Missing the negative sign ignores the directional reality of gravity.
A ball is just allowed to fall from the window of a moving train, it will hit the ground following: [ETEA 2005]
A
Circular path
B
Hyperbolic
C
Straight line path
D
Parabolic path
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
When an object is dropped from a moving frame of reference, it retains the horizontal velocity of that frame due to inertia, while falling under gravity.
Solution:
The combination of constant horizontal velocity and constant vertical acceleration produces a parabolic trajectory.
Why other options are incorrect:
A straight line only occurs if there is no horizontal velocity. Circular and hyperbolic paths do not match projectile kinematics.
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