show that minute hand gains five degree thirty minutes on hour hand in one minute
1 minute is 1/60 of an hour
the minute hand travels 360° in an hour, so it travels 360/60 = 6° in one minute.
The hour hand travels 1/12 as fast as the minute hand. So, in one minute it travels 6/12 ° = 30'
The minute hand thus gains 6°-30' = 5°30'
1hr=60min
In one hr rotation is 360
Hence,hr hand gained 360/60=1/2
Now sutracting 30'because of advancement on hr hand we get ans
5 30'
To demonstrate that the minute hand gains five degrees and thirty minutes over the hour hand in one minute, let's break down and analyze the movements of both hands.
In a clock, the minute hand completes a full rotation, which is 360 degrees, in 60 minutes. Thus, it covers 360 degrees in 60 minutes, which means it moves 6 degrees per minute (360 degrees / 60 minutes = 6 degrees per minute).
On the other hand, the hour hand completes a full rotation in 12 hours, which is equivalent to 720 minutes (12 hours * 60 minutes = 720 minutes). Therefore, it covers 360 degrees in 720 minutes, meaning it moves only 0.5 degrees per minute (360 degrees / 720 minutes = 0.5 degrees per minute).
Now, let's see the difference in movement between the hands over the course of one minute.
During one minute, the minute hand moves 6 degrees, as we determined previously.
The hour hand, however, moves 0.5 degrees per minute. As there are 60 minutes in an hour, it will move 30 degrees in one hour (0.5 degrees per minute * 60 minutes = 30 degrees).
Therefore, the hour hand moves 30/60 = 0.5 degrees in one minute.
When we compare the minute hand's movement of 6 degrees to the hour hand's movement of 0.5 degrees in one minute, we can observe that the minute hand gains 6 - 0.5 = 5.5 degrees on the hour hand.
Thus, we can conclude that the minute hand gains 5 degrees and 30 minutes (or 5.5 degrees) on the hour hand in one minute.