A ball  of mass  is suspended by a thread of length  m. A another ball  of mass  is projected from the ground with velocity  m/s such that at the highest point of its trajectory it collides head–on elastically with ball . It is observed that during subsequent motion, tension in the thread at the highest point is equal to

At highest point of B, the velocity of ball  is
a)	m/s	b)	m/s	c)	m/s	d)	m/s

(a)

Let velocity of ball  at highest point be  then first considering its FBD at this point

Where 

If velocity of ball  just after the collision is  then according to law of conservation of energy,

Its KE at  at highest point

or  m/s

If angle of projection of ball  is , then horizontal component of its velocity will be and it remains constant

Now considering collision of balls  and , let velocities of balls  and , just after the collision, be  and  respectively as shown in Fig.

Then according to the law of conservation of momentum,

      (i)

Since collision is elastic, therefore,

or    (ii)

Solving Eqs.(i) and (ii), we get

Height of initial position of ball  (lowest position)is equal to maximum height ascended by the ball . It is equal to

Height of point of suspension from the ground is