Question

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

Answer 1

Correct Answer - `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^(@)`