Question

The relative angular speed of hour hand and minute hand of clock is

• A. \(\frac{2π}{60}\)
• B. \(\frac{11π}{360}\)
• C. \(\frac{11π}{21600}\)
• D. \(\frac{2π}{3600}\)

Hint:

Find the angular speed of each hand and subtract.

Answer 1

The Correct Option is C

Step 1: Use periods.
The minute hand has period 1 hour and the hour hand has period 12 hours.

Step 2: Relative frequency.
Relative frequency = $\dfrac{1}{1\text{ h}} - \dfrac{1}{12\text{ h}} = \dfrac{11}{12\text{ h}^{-1}}$, so one overtaking takes $12/11$ hours.

Step 3: Angular speed.
$\omega_{rel} = \dfrac{2\pi}{(12/11)\times 3600\text{ s}} = \dfrac{22\pi}{43200} = \dfrac{11\pi}{21600}$ rad/s.

Final Answer:
Option (C). \[ \boxed{\frac{11\pi}{21600}} \]