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Two identical small balls A and B each of mass m connected by a light inextensible string of length l are placed on a frictionless horizontal floor. With what velocity u must the ball B be projected vertically upwards so that the ball A leaves the floor?
Asked by pratham.k | 02 Jun, 2020, 00:20: AM
answered-by-expert Expert Answer
Consider the state when the B is above the ball A when it is still touching the ground. 
To lift ball A, the tension in string must be greater than its weight 
 
T space greater or equal than space m g space... space left parenthesis 1 right parenthesis A s space b a l l space B space i s space i n space c i r c u l a r space m o t i o n space a r o u n d space b a l l space A comma space t h e space t e n s i o n space w i l l space b e space e q u a l space t o space c e n t r i p e t a l space f o r c e. space fraction numerator m v squared over denominator calligraphic l end fraction space greater or equal than m g rightwards double arrow v greater or equal than space square root of g calligraphic l end root space... space left parenthesis 2 right parenthesis O n space e q u a t i n g space i n i t i a l space a n d space f i n a l space t o t a l space e n e r g y space o f space t h e space b a l l 1 half m u squared space equals space 1 half m v squared plus thin space m g calligraphic l therefore u squared equals v squared plus 2 g calligraphic l f r o m space left parenthesis 2 right parenthesis comma space therefore u squared greater or equal than space g calligraphic l plus 2 g calligraphic l therefore u squared greater or equal than 3 g calligraphic l therefore u space greater or equal than space square root of 3 g calligraphic l end root space
Answered by Shiwani Sawant | 02 Jun, 2020, 16:02: PM
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