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Question

A body of mass 2 kg moving with a velocity 3 m/s collides with a body of mass 1 kg moving with a velocity of 4 m/s in opposite direction. If the collision is head on and completely inelastic, then

A
Both particles move together with velocity (23)m/s
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B
The momentum of system is 2kg m/s throughout
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C
The momentum of system is 10 kg m/s
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D
The loss of KE of system is (493)J
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Solution

The correct option is D The loss of KE of system is (493)J
In completely inelastic collision,
m1u1m2u2=(m1+m2)V
2×31×4=(2+1)V;V=23m/s
Net momentum of system P=m1u1m2u2
2×31×4=2 kg m/s
Loss in KE=12m1u21+12m2u2212(m1+m2)V2
=12×2×(3)2+12×(1)×(4)212×(2+1)×(23)2
=9+823=1723=493J

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