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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, the percentage loss in the energy during the collision is close to

A
50%
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B
56%
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C
62%
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D
44%
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Solution

The correct option is B 56%
As the collision is inelastic the masses will move together
Assuming the speed of block A and B becomes v1^i+v2^j
Writing momentum equation in x direction
m(2v)+2m(0)=3mv1v1=2v3
Writing momentum equation in Y direction
m(0)+2m(v)=3mv2v2=2v3
The velocity of both blocks will be 2v3^i+2v3^j

So,
Einitial=12m(2v)2+122m(v)2=3mv2
Efinal=123m(49v2+49v2)=43mv2
Therefore the fractional loss is
EinitialEfinalEinitial×100=3433×100

=59×100
=56%

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