Physics Rotational & Circular Motion MDCAT 2010
PMDC Verified Question 92 of 95
A wheel of radius \( 1 \text{ m} \) covers an angular displacement of \( 180^\circ \). Its linear displacement is:
A
\( 3.14 \text{ m} \)
B
\( 6.28 \text{ m} \)
C
\( \pi \text{ rad} \)
D
\( 0.157 \text{ m} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( 3.14 \text{ m} \)
Concept:

Linear displacement (arc length) relates to angular displacement, but the angle must first be converted from degrees into radians.

Formula:

$$ S = r\theta $$

Solution:

  • Convert \( 180^\circ \) to radians: \( 180^\circ = \pi \text{ radians} \).
  • Given radius \( r = 1 \text{ m} \).
  • Calculate the arc length: \( S = (1 \text{ m})(\pi \text{ rad}) = \pi \text{ m} \).
  • Since \( \pi \approx 3.14 \), the linear displacement is \( 3.14 \text{ m} \).


Why other options are incorrect:

  • Option B incorrectly uses \( 360^\circ \) or \( 2\pi \).
  • Option C is a unit of angle, not a unit of linear distance.
  • Option D is a calculation error involving improper conversion factors.

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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