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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.EiK.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=3mv243mv23mv2×100
=59×10055.55%
Hence it is approximately 56%.

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