CBSE Class 11-science Answered
find the ratio of average speed and magnitude of average velocity of tip of a minute hand in 20 minutes
Asked by ukalyadab | 18 Jul, 2022, 11:52: AM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/58c41750587855e7cdac854251074f5c62d50b9790d9d7.61962187f2.png)
Average speed = distance / time
distance travelled by minute hand in 20 s = (1/3) (2πR )
where R is length of minute hand.
Average speed = [ (1/3) (2πR )] / ( 20 × 60 ) = ( π / 1800 ) R m/s
-------------------------------------------------
Average velocity = displacement / time
Since the motion is on a plane , Average velocity has two components
Average x-velocity vx = x-displacement / time
( Polar coordinates are used to get displacements )
Average x-velocity vx = [ R cos330 - R cos90 ] / (20×60) = ( √3 / 2400 ) R m/s
Average y-velocity vy = y-displacement / time
Average y-velocity vy = [ R sin330 - R sin90 ] / (20×60) = ( -3 / 2400 ) R m/s
magnitude of Average velocity v =
m/s
![begin mathsize 14px style square root of v subscript x superscript 2 plus v subscript y superscript 2 end root space equals space 1 over 2400 open parentheses square root of 3 plus 9 end root close parentheses space R space equals space fraction numerator square root of 3 over denominator 1200 end fraction R end style](https://images.topperlearning.com/topper/tinymce/cache/012a1ff8f2d08d7391327337bedbb782.png)
Ratio of average speed to magnitude of average velocity is determined as follows
![begin mathsize 14px style R a t i o space equals space fraction numerator pi divided by 1800 over denominator square root of 3 space divided by space 1200 end fraction space equals space fraction numerator 2 space pi over denominator 3 space square root of 3 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/e5ff84d6757d0cc809032e1cf0f42d70.png)
Answered by Thiyagarajan K | 18 Jul, 2022, 13:31: PM
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