# A ball of mass  is hung vertically by a thread of length  m. Upper end of the thread is attached to the ceiling of a trolley of mass . Initially, the trolley is stationary and it is free to move along horizontal rails without friction. A shell of mass  moving horizontally with velocity collides with the ball and gets stuck with it. As a result, the thread starts to deflect towards right The velocity of the combined body just after collision is a) 2 m/s b) 3 m/s c) 1 m/s d) 4 m/s

## Question ID - 101260 :- A ball of mass  is hung vertically by a thread of length  m. Upper end of the thread is attached to the ceiling of a trolley of mass . Initially, the trolley is stationary and it is free to move along horizontal rails without friction. A shell of mass  moving horizontally with velocity collides with the ball and gets stuck with it. As a result, the thread starts to deflect towards right The velocity of the combined body just after collision is a) 2 m/s b) 3 m/s c) 1 m/s d) 4 m/s

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(b)

When shell strikes the ball and gets stuck with it, combined body of mass  starts to move to the right. Let velocity of the combined body (just after collision) be . According to law of conservation of momentum,

As soon as the combined body starts to move rightwards, thread becomes inclined to the vertical. Horizontal component of its tension retards to the combined body while trolley accelerates rightwards due to the same component of tension

Inclination of thread with the vertical continues to increase till velocities of both (combined body and trolley) become identical or combined body comes to rest relative to the trolley. Let velocity at that instant of maximum inclination of thread be . According to law of conservation of momentum,

or

During collision of ball and shell, a part of energy is lost. But after that there is no loss of energy. Hence, after collision, kinetic energy lost is used up in increasing gravitational potential energy of the combined body

If maximum inclination of threads with the vertical is , then according to law of conservation of energy

or

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