Question

The ratio of the angular speed of the minute hand to the second hand of a watch is?

• A. \( 1 : 60 \)
• B. \( 1 : 3600 \)
• C. \( 1 : 360 \)
• D. \( 1 : 120 \)

Hint:

The second hand of a watch moves 60 times faster than the minute hand, giving a ratio of angular speeds of \( 1 : 3600 \).

Answer 1

The Correct Option is B

The angular speed \( \omega \) is given by the formula: \[ \omega = \frac{\Delta \theta}{\Delta t} \] Where \( \Delta \theta \) is the change in angle, and \( \Delta t \) is the time taken. - The minute hand completes one full rotation (360°) in 60 minutes, so its angular speed is: \[ \omega_{\text{minute}} = \frac{360^\circ}{60 \times 60 \, \text{s}} = \frac{360^\circ}{3600 \, \text{s}} = \frac{1^\circ}{10 \, \text{s}} \] - The second hand completes one full rotation (360°) in 60 seconds, so its angular speed is: \[ \omega_{\text{second}} = \frac{360^\circ}{60 \, \text{s}} = 6^\circ/\text{s} \] The ratio of the angular speed of the minute hand to the second hand is: \[ \frac{\omega_{\text{minute}}}{\omega_{\text{second}}} = \frac{\frac{1^\circ}{10 \, \text{s}}}{6^\circ/\text{s}} = \frac{1}{3600} \] Thus, the correct answer is \( 1 : 3600 \).