For a smoothly running analog clock, the ratio of the number of rotations made in a day by the hour hand to th

Question

For a smoothly running analog clock, the ratio of the number of rotations made in a day by the hour hand to the second hand, respectively, is:

Accepted Answer

1.  **Analyze the Motion of the Hour Hand:**
    *   The hour hand completes one full rotation in 12 hours.
    *   In one day (24 hours), the number of rotations made by the hour hand is:
        $$ N_{hour} = \frac{24 	ext{ hours}}{12 	ext{ hours/rotation}} = 2 	ext{ rotations} $$

2.  **Analyze the Motion of the Second Hand:**
    *   The second hand completes one full rotation in 1 minute.
    *   There are $24 	imes 60 = 1440$ minutes in a day.
    *   Therefore, in one day, the number of rotations made by the second hand is:
        $$ N_{second} = 1440 	ext{ rotations} $$

3.  **Calculate the Ratio:**
    *   The ratio of the number of rotations of the hour hand to the second hand is:
        $$ 	ext{Ratio} = \frac{N_{hour}}{N_{second}} = \frac{2}{1440} $$
    *   Simplifying the fraction:
        $$ 	ext{Ratio} = \frac{1}{720} $$
    *   Thus, the ratio is $1:720$.

Step-by-Step Solution

Practice All PHYSICS Questions