Question

Show that the minute hand of a watch gains 5°30' on the hour hand in a minute

Answer 1

In 1 minute, hour hand moves= 0.5°
and minute hand moves= 6°
Hence in 1 minute, the minute hand gains =6-0.5= 5.5° or 11/2 degrees over the hour hand.

Answer 2

Gain by minute hand is 5.5 degrees

To find:

Gain by other minute hand

Given:  

Minute hand of a watch gains 5°30'  

Solution:

It is a fact that clock has two hands i.e. the smaller one is known as the hour hand and the longer one is known as minute hand. It is circular and so it is 360 degree round.

Time taken by a hour hand to complete 360 degrees $=12 \times 60= 720$minutes

while time taken by a minute hand to complete 360 degrees = 60 minutes

Hence, in one minute

Hour hand $=\frac{360}{720}= 0.50$ degrees

Minute hand $=\frac{360}{60}$ = 6.00 degrees

Therefore, gain by minute hand = 6 - 0.5 = 5.5 degrees