Physics Rotational & Circular Motion SZABMU 2022
PMDC Verified Question 52 of 95
Which one of the following is the angular velocity of an electric motor if it runs at \( 400 \text{ rpm} \)?
A
\( 51.2 \text{ rads}^{-1} \)
B
\( 41.9 \text{ rads}^{-1} \)
C
\( 45.2 \text{ rads}^{-1} \)
D
\( 38.5 \text{ rads}^{-1} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 41.9 \text{ rads}^{-1} \)
Concept:

To convert RPM (revolutions per minute) into SI units (radians per second), we multiply by \( 2\pi \) and divide by 60.

Formula:

$$ \omega = \text{rpm} \times \frac{2\pi}{60} $$

Solution:

  • Given \( 400 \text{ rpm} \).
  • \( \omega = 400 \times \frac{2\pi}{60} \).
  • Simplify: \( \omega = \frac{800\pi}{60} = \frac{80\pi}{6} = \frac{40\pi}{3} \).
  • Substitute \( \pi \approx 3.1416 \): \( \omega = \frac{40(3.1416)}{3} \approx \frac{125.66}{3} \).
  • Calculate division: \( 41.88 \text{ rad/s} \).
  • Rounds best to \( 41.9 \text{ rads}^{-1} \).


Why other options are incorrect:

  • Option A, Option C, Option D are mathematically off. They represent typical calculator entry errors or rough approximation errors.

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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