A sphere of mass `m` collides against a pendulum of mass `m` with horizontal velocity `upsilon_90)`. (i) Calculate the maximum height reached by the pendulum if the masses scatter elastically along the line of initial motion, (ii) What is the maximum height reached by the pendulum if the two masses stick together ?

Explanation

As the collision is perfectly elastic, the total `K.E.`, is transferred to the ball of the pendulum, Figure, If `h` is maximum height reached by the pendulum, then as `P.E.=K.E.`
`mgh=(1)/(2)m upsilon_(0)^(2)`
`h=(upsilon_(0)^(2))/(2g)`
(ii) When the two masses stick together, velocity of the combination `(V)` is obtained from principle of conservation of linear momentum, i.e.,
`(2m)V=mxxupsilon_(0)+0, V=(upsilon_(0))/(2)`
`,. h=(V^(2))/(2g)=((upsilon_(0)//2)^(2))/(2g)=(upsilon_(0)^(2))/(8g)`