Physics Rotational & Circular Motion ETEA 2016
PMDC Verified Question 88 of 95
A child riding on a large merry-go-round, travels a distance of \( 3000 \text{ m} \) in a circle of diameter \( 40 \text{ m} \). The total angle through which she revolves is:
A
\( 50 \text{ rad} \)
B
\( 75 \text{ rad} \)
C
\( 150 \text{ rad} \)
D
\( 314 \text{ rad} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 150 \text{ rad} \)
Concept:

The total angle revolved by an object is exactly equal to the total distance traveled along the arc divided by the radius of the circular path.

Formula:

$$ \theta = \frac{S}{r} $$

Solution:

  • The diameter is \( 40 \text{ m} \), so the radius \( r \) is \( \frac{40}{2} = 20 \text{ m} \).
  • The linear distance traveled \( S = 3000 \text{ m} \).
  • Divide distance by radius: \( \theta = \frac{3000}{20} = 150 \text{ radians} \).


Why other options are incorrect:

  • Option B (75 rad) mistakenly uses the diameter (40m) instead of the radius in the denominator.
  • Option A and Option D result from using incorrect formulas involving \( \pi \) unnecessarily.

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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