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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
answered-by-expert Expert Answer
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 = 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  m/s
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
 
Answered by Thiyagarajan K | 18 Jul, 2022, 13:31: PM

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