A small ball of mass `m_(2)` rests on the top of a bigger ball of mass `m_(1)(gtgtm_(2)`. The centre of bigger ball is at height `3r` above ground as shown. The balls are dropped from this situation. If the smaller ball bounces to a height 4 nr from ground after its first collision with bigger ball. find n. (Assume all collisions are elastic).

Answer

5

Explanation

Velocity of ball m, just after collision with ground
`u_(1)=sqrt(4gr)`
Velocity of ball `m_(2)` at this instant is `u_(2)=-sqrt(4gr)`
Velocity of `m_(2)` just after collision between `m_(1)&m_(2)`
`V_(2)=-U_(2)+2u_(1)=sqrt(4gr)+2sqrt(4gr)=3sqrt(4gr)`
max height bt `m_(2)=2r+(v_(2)^(2))/(2g)=20r`