A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two-body centre of mass is x/(10) m/s. Then the value of x is .

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Accepted Answer

25. The centre of mass velocity never changes in a collision, so it can be read off from the state before impact — but the second mass is needed first. Momentum: 2(4)=2(1)+m₂v₂, so m₂v₂=6. Elastic, so kinetic energy is conserved: 1/2(2)(16)=1/2(2)(1)+1/2 m₂v₂², giving m₂v₂²=30. Dividing: v₂=(30)/6=5 m/s, hence m₂=6/5=1.2 kg. v_cm=(2(4))/(2+1.2)=8/(3.2)=2.5 m/s. Comparing with x/(10) gives x=25.

A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its initial speed. The speed of the two-body centre of mass is x/(10) m/s. Then the value of x is ______.

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