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Question

Two perfectly elastic balls of the same mass m are moving with velocities u1 and u2. They collide head on elastically, n times. The kinetic energy of the sytem finally is

A
12mnu21
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B
12mn(u21+u22)
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C
12m(u21+u22)
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D
12mn(u21+u22)
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Solution

The correct option is C 12m(u21+u22)
As we know,
In elastic collision kinetic energy of the system remains same before and after the collision.
Hence after the collision, KE will be same as the initial kinetic energy before the collision.
Therefore, kinetic energy after n collisions=12mu21+12mu22=12m(u21+u22)

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