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A ball of mass in m= 1 kg is hung vertic...

A ball of mass in `m= 1 kg` is hung vertically by a thread of length `l = 1.50 m`. Upper end of the thread is attached to the ceiling of a trolley of mass `M= 4 kg`. Initially, the trolley is stationary and it is free to move along horizontal rails without friction. A shell of mass `m=1 kg`, moving horizontally with velocity `v_(0 )= 6 m//s` collides with the ball and gets stuck with it. As a result, the thread starts to deflect towards right.

At the time of maximum deflection of the thread with vertical, the trolley will move with velocity

Text Solution

Verified by Experts

The correct Answer is:
`37^(@)`
`COLM : mv_(0) = (M + 2m) v_(1)`
`v_(1) = (mv_(0))/(m) = (v_(0))/(6) = 1 m//s`
`COME : rArr (1)/(2) (2m) ((v_(0))/(2))^(2) = (1)/(2) Mv_(1)^(2) + 2m xx g xx h + (1)/(2)(2m)v_(1)^(2)`
`rArr h = 0.3 m = L (1 - cos theta)`
`cos theta = 1 - (3)/(15) = (4)/(5) rArr 0 = 37^(@)`
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