Physics Rotational & Circular Motion DUHS 2022
PMDC Verified Question 64 of 95
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
\( a_c = \frac{4\pi^2 r}{T} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( a_c = \frac{4\pi^2 r}{T^2} \)
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.

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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