A sphere of mass 2 kg moving with a velocity collides elastically with another sphere which is at rest. If after the collision, the first sphere moves in the same direction with its velocity reduced to one third of its initial velocity, find the mass of the second sphere.

Explanation

Here `m_(1)=2kg, u_(1)=u_(1),u_(2)=0, v_(1)=(1)/(3)u_(1)`
In elastic collisions
`v_(1)=((m_(1)-m_(2))/(m_(1)+m_(2)))u_(1)+((2m_(2))/(m_(1)+m_(2)))u_(2)`
`=((2-m_(2))/(2+m_(2)))u_(1)+((2m_(2))/(2+m_(2)))xx0`
But `v_(1)=(1)/(3)u_(1) " " therefore (1)/(3)u_(1)=((2-m_(2))u_(1))/(2+m_(2))`
`2+m_(2)=6-3m_(2), 4m_(2)=4` or `m_(2)=1kg`