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Question

A ball of mass m moving with speed u undergoes a head-on elastic collision with a ball of mass nm initially at rest, the ratio of the kinetic energies of the first ball to the second ball after collision is

A
(1n)22n
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B
(1n)24n
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C
(1+n)22n
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D
(1+n)24n
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Solution

The correct option is B (1n)24n
By conservation of momentum
mu=mu1+nmu2u=u1+nu2(1)
Co-efficient of restitution
u0=u2u1(2)(2)in(1)u2=2un+1&u1=(1n)un+1KEF1KEF2=1/2mu211/2nmu22=u21nu22=(1n)24n

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