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Question

A ball of mass m moving with speed u undergoes a head on collision with a stationary ball of mass 3m. If collision is perfectly inelastic, find the loss of kinetic energy.

A
14mu2
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B
18mu2
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C
116mu2
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D
38mu2
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Solution

The correct option is D 38mu2
For inelastic collision, both ball will move together with speed v after collision.
Now, applying momentum conservation,
mu+0=(m+3m)v
v=u4
Initial kinetic energy =12mu2
Final kinetic energy =12(m+3m)v2
=12(4m)(u4)2
=18mu2
So, Loss in KE = Initial KE - Final KE
=12mu218mu2
=38mu2

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