Question

The ratio of angular speed of a second-hand to the hour-hand of a watch is

• A. 3600 : 1
• B. 720 : 1
• C. 72 : 1
• D. 60 : 1

Answer 1

The correct option is B 720 : 1

We know that a second hand of the clock takes 60sec (1 min) to cover an angular distance of 2$\pi$ radians (360°).

Therefore angular speed = $\frac{2\pi }{60}rad/sec$

= $\frac{\pi }{30}$

For an hour hand to complete 1 rotation i.e 2$\pi$ radians it takes 12hrs ( 12×3600 seconds).

Therefore angular speed of an hour hand =$\frac{2\pi }{43200}$

= $\frac{\pi }{21600}$

Finally the required ratio of angular speed of the second hand to the houe hand = $\frac{\frac{\pi }{30}}{\frac{\pi }{21600}}$

=$\frac{21600}{30}=\frac{720}{1}=720:1$