Question

For a smoothly running analog clock, the ratio of the angular velocity of the minute hand to the angular velocity of the hour hand is

• A. 2
• B. 12
• C. 24
• D. 60
• E. 360

Hint:

In problems involving rotating objects, remember that the angular velocity is proportional to the number of rotations per unit time.

Answer 1

The Correct Option is B

The angular velocity of a rotating object is given by the formula: \[ \omega = \frac{\theta}{t} \] where \(\theta\) is the angle moved in time \(t\). In a clock, the hour hand completes one full revolution (360°) in 12 hours, so its angular velocity is: \[ \omega_{{hour}} = \frac{360°}{12 \, {hrs}} = 30°/{hr} \] The minute hand completes one full revolution (360°) in 60 minutes (or 1 hour), so its angular velocity is: \[ \omega_{{minute}} = \frac{360°}{1 \, {hr}} = 360°/{hr} \] The ratio of the angular velocities is: \[ \frac{\omega_{{minute}}}{\omega_{{hour}}} = \frac{360}{30} = 12 \] Hence, the correct answer is (B).