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Question

A juggler keeps n balls going with one hand, so that at any instant, (n-1) balls are in air and one ball in the hand. If each ball rises to a height of x metres, the time for each ball to stay in his hand is

A
1n12xg
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B
2n12xg
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C
2n2xg
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D
1n2xg
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Solution

The correct option is C 2n12xg
Let u be the initial velocity of the ball while going upwards.
The final velocity of the ball at height x is, v=0
Using the relation; v2=u2+2as
we have,
0=u22gxu=2gx
If t is the time taken by the ball in going up through distance x,
then 0=u+(g)tt=ug
​Total time after which the ball comes into the hand is :
T=2t=2ug=22xg

During time T, (n1) balls will be in air and one ball will be in hand.

TIme of stay for each ball in hand , =Tn1=22xgn1=2(n1)2xg
Hence, the correct option is (B)

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