Question

The relative angular speed of hour hand and second hand of a clock is

• A. \( \frac{359 \pi}{21600} \)
• B. \( \frac{719 \pi}{21600} \)
• C. \( \frac{11 \pi}{21600} \)
• D. \( \frac{9 \pi}{21600} \)

Hint:

To find the relative angular speed, subtract the angular velocities of the two moving parts, considering their respective time periods.

Answer 1

The Correct Option is B

Step 1: Understanding the motion of clock hands.
The hour hand makes one full rotation (i.e., \( 2 \pi \) radians) in 12 hours, and the second hand makes one full rotation (i.e., \( 2 \pi \) radians) every 60 seconds. - Angular speed of hour hand: \[ \omega_{\text{hour}} = \frac{2 \pi}{12 \times 3600} = \frac{\pi}{21600} \, \text{radians per second} \] - Angular speed of second hand: \[ \omega_{\text{second}} = \frac{2 \pi}{60} = \frac{\pi}{30} \, \text{radians per second} \] Step 2: Calculating the relative angular speed.
The relative angular speed is the difference between the angular speeds of the second hand and the hour hand: \[ \omega_{\text{relative}} = \omega_{\text{second}} - \omega_{\text{hour}} = \frac{\pi}{30} - \frac{\pi}{21600} \] Simplifying this: \[ \omega_{\text{relative}} = \frac{719 \pi}{21600} \] Thus, the correct answer is (B) \( \frac{719 \pi}{21600} \).