Physics Rotational & Circular Motion MDCAT 2017
PMDC Verified Question 82 of 95
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 \( 81 \text{ cm/s} \)?
A
\( 6 \text{ cm} \)
B
\( 9 \text{ cm} \)
C
\( 3 \text{ cm} \)
D
\( 7 \text{ cm} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 3 \text{ cm} \)
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 \( t=6 \).

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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