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

Options

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

Answer

C

Explanation

The second - hand completes one rotation in 1 min and the hour - hand completes in 12 h .
` :. ` The angular speed of the second - hand is
` omega_(s) = (2pi " rad")/(1 "min") = (2pi "rad")/(60s)`
and that of the hour - hand is
` omega_(h) = (2pi "rad")/(12 h ) = ((2pi "rad"))/(12 xx 60 xx 60 s )`
Their corresponding ratio is
` (omega_(s))/(omega_(h)) = ((2pirad)/(60s))/((2pi rad)/(12xx 60 xx 60 s)) = (12 xx 60 xx 60 )/60 = 720 / 1 `