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

The ratio of the angular speed of the second's hand to the hour hand of the clock can be calculated as follows:

The second's hand completes one full rotation (360 degrees) in 60 seconds because there are 60 seconds in a minute.

The hour hand completes one full rotation (360 degrees) in 12 hours because there are 12 hours on a clock.

Now, to find the ratio of their angular speeds, you need to compare the angles covered by each hand in the same amount of time. Let's say we want to find the ratio for 1 second.

The second's hand covers 360 degrees in 60 seconds, so in 1 second, it covers 360/60 = 6 degrees.

The hour hand covers 360 degrees in 12 hours, which is equivalent to 12 * 60 = 720 minutes. So in 1 minute, it covers 360/720 = 0.5 degrees.

Now, we have the angular speeds for both hands in 1 second:

Second's hand: 6 degrees/second
Hour hand: 0.5 degrees/second
To find the ratio, we divide the angular speed of the second's hand by the angular speed of the hour hand:

Ratio = (Angular speed of second's hand) / (Angular speed of hour hand) = 6 degrees/second / 0.5 degrees/second = 12

So, the ratio of the angular speed of the second's hand to the hour hand of the clock is 12, which corresponds to option (A) in the given choices.