Question

Ratio of angular speed of second’s hand to the hour hand of the clock is?
(A) 12
(B) 60
(C) 720
(D) 180

Answer 1

Hint: We need to find the ratio of the angular speed. We know there are two types of speed for a body in a circular motion. One is the linear velocity and the other is angular velocity. Angular velocity is defined as the rate of change of the angle of the body. We know that both the minute and the hour hand cover an angle of ${{360}^{0}}$in one complete revolution.

Complete step by step answer:
For hour hand:
Angle covered$=2\pi $
Time taken$=12h$, changing into seconds we get, $=12\times 60\times 60=43200s$
Angular velocity $\omega =\dfrac{2\pi }{43200}$
For second’s hand:
Angle covered$=2\pi $
Time taken$=1\min $, changing into seconds we get, $=1\times 60=60s$
Angular velocity $\omega =\dfrac{2\pi }{60}$
Taking the ratio, we get, $\dfrac{\dfrac{2\pi }{60}}{\dfrac{2\pi }{43200}}=\dfrac{43200}{60}=720$

So, the correct option is C.

Note:While calculating the angular velocity we need to keep in mind that angle is always to be taken in radians and not in degrees. The second hand completes one revolution in the 60s, while the minute hand completes one revolution in 60 minutes and for the hour hand to start from 12 and again come back to 12, it takes 12 hours. The angle covered in all the cases is the same. mind the standard SI unit of angular velocity is rev/sec. Also, if some question says that the value of angular velocity is /sec, then it does not talk about angular velocity but it talks about frequency and to get angular velocity from frequency we have to use the formula, \[w=2\pi f\].