Question

The ratio of the magnitudes of angular velocity of the hour hand a watch to that of earth's rotation about its own axis is

• A. 1 : 1
• B. 1 : 2
• C. 1 : 3
• D. 2 : 1

Answer 1

The correct option is D 2 : 1

Hour hand of a watch or a clock turns 1 complete circle in 12 hours. Its angular velocity$,{\omega }_1=\frac{2\pi }{12}\text{hours}=\frac{\pi }{6}$ radians / hour

Angular velocity of revolution of earth around its own axis ${\omega }_2=\frac{2\pi }{24}$ hours

$=\frac{\pi }{12}$ radians / hour

Because it takes $24$ hours to complete 1 complete circle .

Required ratio,$\frac{{\omega }_1}{{\omega }_2}=2:1$