In an electric clock the extremity of the hour hand moves one twentiech as fast as that of the minute hand . What is the length of the hour if the minute hand is 10 cm long ?

Explanation

The angular speed of the hour hand , `omega^(H) = (2pi)/(3600 xx 12)` rad /sec
The angular speed of the minute hand , `omega_(M) = (2pi)/(3600)` rad/sec .
Let `r_(H)` be the length of the hour hand .
`therefore` The linear speed of the extremity of the hour hand is given by v = `r omega`
`therefore v _(H) = r_(H) omega_(H)`
Similary , for the minute hand ,
`V_(M) = r_(M) omega_(M)`
Now , by problem , `v_(H) = (1)/(20) v_(M) or r_(H) omega_(H) = (1)/(20) r_(M) omega_(M)`
`therefore r_(H) xx (2pi)/(3600 xx 12) = (1)/(20) xx 10 xx (2pi)/(3600) or r_(H) = 6` cm