Physics Rotational & Circular Motion NUMS 2023
PMDC Verified Question 43 of 95
In case of centripetal force the value of instantaneous acceleration is given by:
A
\( a_c = \frac{v}{r} \)
B
\( a_c = \frac{v^2}{r} \)
C
\( a_c = vr \)
D
\( a_c = v^2r \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( a_c = \frac{v^2}{r} \)
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.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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