Physics Rotational & Circular Motion MDCAT 2018
PMDC Verified Question 80 of 95
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
A
\( 4 \text{ rad} \)
B
\( 12 \text{ rad} \)
C
\( 9 \text{ rad} \)
D
\( 7 \text{ rad} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 9 \text{ rad} \)
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.

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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