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Question

A sphere of mass m1 in motion hits directly another sphere of mass m2 at rest and sticks to it, the total kinetic energy after collision is 2/3 of their total K.E before the collision. Find the ratio m1:m2.

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Solution

Velocity after collision is v1.
m1v=(m1+m2)v1v1=m1(m1+m2)v
K.E before collision=32 k.e after collision.
12m1v2=32×12(m1+m2)v12m1v2=32×m12(m1+m2)v22(m1+m2)=3m12m2=m1m1m2=2

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