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Question

A particle of mass m moving in the direction x 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
  1. 44%
  2. 50%
  3. 62%
  4. 56%

A
56%
B
62%
C
44%
D
50%
Solution
Verified by Toppr

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
The loss in kinetic energy
12m(2v)2+122m(v)2123m(22v3)2
3mv243mv2=53mv2
percentage loss53mv23mv2×100=56 %

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