    Question

# A particle of mass m moving in the x− direction with speed 2v is hit by another particle of mass 2m moving in the y− direction with speed v. If the collision is perfectly inelastic, then loss in energy(%) during the collision is close to

A
40%
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B
50%
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C
56%
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D
62%
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Solution

## The correct option is C 56%Since, there is no external force during the collision, momentum along x & y direction will remain conserved. Both the particles will stick together as a mass 3m, since it is a perfectly inelastic collision. Considering the mass 3m to have velocity vx & vy along x and y directions after collision, Using PCLM along x− direction gives, Pi=Pf m(2v)=(3m)vx PCLM along y− direction gives, 2m(v)=3m(vy) ∴vy=23v % loss in K.E =K.Ei−K.EfK.Ei×100 (K.E)i=12(2m)v2+12m(2v)2 ⇒(K.E)i=3mv2 (K.E)f=12(3m)(v2x+v2y) =12(3m)[(23v)2+(23v)2] =12(3m)(89v2) ⇒(K.E)f=43mv2 % loss in K.E=3mv2−43mv23mv2×100 =59×100≃55.55% Hence it is approximately 56%.  Suggest Corrections  1      Similar questions
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