A pan of mass kg and a block of mass  are connected to each other by a light inextensible string, passing over a light pulley as shown in Fig. Initially, the block is resting on a horizontal floor. A ball of mass  collides with the pan at a speed  Consider this instant of collision at  Assume collision to be perfectly inelastic. Now, answer the following questions based on the above information

Mark the correct statement(s) for this situation
a)	After the collision, the pan + ball system moves downwards with decreasing speed
b)	After the collision, the block is moving upwards with the same speed with which the ball + pan system is moving downwards
c)	The block will jerk for a number of times during its motion
d)	All of these

(d)

Due to collision, an impulsive tension occurs in the string

For ball + pan system,

For block,

As the string is taut and the mass of the block is greater than the mass of ball + pan, so the block and ball + pan are under deceleration, given by

So, block will again come to ground after time , given by

At this instant, the pan + ball system is moving with  and the string gets slacked, so the system is moving under gravity

To determine the speed of the system at , first find the time after which string is again jerked. That will happen when pan + ball system crosses its instant during its downward journey, i.e., after itstime of flight of motion under gravity

i.e., string will again jerk at

For , the system is again under a retardation of

Before this, find the velocity of various components of system just after jerk. We have

and

With this velocity, the ball + pan system moves down for 0.2 s under a retardation of 

 (downwards)

The maximum height attained by the block after the second jerk is given by