MHT CET · Physics · Rotational Motion

The relative angular speed of hour hand and minute hand of a clock is (in rad/s)

A \(\frac{9 \pi}{1860}\)
B \(\frac{11 \pi}{21600}\)
C \(\frac{4 \pi}{243}\)
D \(\frac{7 \pi}{1480}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{11 \pi}{21600}\)

Step-by-step Solution

Detailed explanation

We know angular speed of the hour and minute hand of the clock are given by, \(\omega_h=\frac{2 \pi}{12 \times 3600}\) and \(\omega_m=\frac{2 \pi}{3600}\) respectively.
Therefore, the relative angular velocity is just the difference between these values:
\(\Delta \omega=\frac{2 \pi}{3600}-\frac{2 \pi}{12 \times 3600}=\frac{2 \pi}{3600}\left(\frac{11}{12}\right)=\frac{11 \pi}{21600}\) radians per second

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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