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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 2 kg 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 K.E. of system is (493) J
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Solution

## The correct option is D The loss of K.E. of system is (493) JIn completely inelastic collision, bodies coalesce m1u1−m2u2=(m1+m2)V 2×3−1×4=(2+1)V; V=23 m/s Net momentum of system P=m1u1−m2u2 2×3−1×4=2 kg~m/s Loss in KE =12m1u21+12m2u22−12(m1+m2)V2 =12×2×(3)2+12×(1)×(4)2−12×(2+1)×(23)2 =9+8−23=17−23=493 J

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