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Question

A spherical ball of mass 1 kg moving with a uniform speed of 1 m/s collides symmetrically with two identical spherical balls of mass 1 kg each at rest touching each other. If the two balls move with 0.5 m/s in two directions at the same angle of 60o with the direction of the first ball, the loss of kinetic energy on account of the collision is?

A
0.125 J
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B
0.5 J
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C
1.0 J
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D
0.75 J
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Solution

The correct option is A 0.125 J
Initial momentum (before collision),
P1= 1kg×1 m/s= 1kg m/s
Initial kinetic energy, K.E1= 12×1×1
=0.5 J
After collision, the two stationary balls start moving at an angle of 60o. and the first ball moving with a velocity (say v)
From conservation of momentum
1= 1×0.5cos60o+1×0.5Cos60o+1×v
1= 0.5+v
v=0.5 m/s
Kinetic energy after collision, K.E2=12×1×(0.5)2+12×1×(0.5)2+12×1×(0.5)2
= 32×(0.5)2
= 0.375J
Loss in K.E= K.E1K.E2
=(0.5-0.375)J
= 0.125J

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