A body of 2 kg mass makes an elastic collision with another body at rest. The velocity of the 2 kg mass is reduced to one-fourth of the original velocity. However, direction remains unchanged. What is the mass of the body struck?
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Using formula for elastic collision when the target (i.e. second body here) is at rest before collision.
v1 = (m1 - m2)/(m1 + m2) * u1
It is given v1 = u1/4 and substituting the value m1 = 2.0 kg,
u1/4 = (2 - m2)/(2 + m2) * u1
Divide by u1
1/4 = (2 - m2)/(2 + m2)
Or 2 + m2 = 4 * (2 - m2)
Or 2 + m2 = 8 - 4m2
Or m2 + 4m2 = 8 - 2
Or 5m2 = 6
Or m2 = 6/5 = 1.2 kg
Ans: 1.2 kg
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