The ratio of angular speed of the minute hand of clock to that of its hour hand is:

Explanation

The clock displays 12 divisions, which are 1 hour each for the hour hand and 5 minutes each for the minute hand. The minute hand completes 1 whole rotation of the 12 divisions for the hour hand to move 1 whole division; hence, the minute hand has to be 12 times faster than the hour hand.The minute hand of a clock completes one revolution (360 degrees) in one hour or 60 minutes. Therefore, its angular speed isωminute = (360 degrees) / (60 minutes) = 6 degrees per minuteThe hour hand of a clock completes one revolution in 12 hours or 720 minutes. Therefore, its angular speed is:ωhour = (360 degrees) / (720 minutes) = 0.5 degrees per minuteThe ratio of the angular speed of the minute hand to that of the hour hand is:ωminute / ωhour = (6 degrees per minute) / (0.5 degrees per minute) = 12Therefore, the ratio of the angular speed of the minute hand to that of the hour hand is 12:1.