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Question

# A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body ?

A
1.2 kg
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B
1 kg
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C
1.5 kg
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D
1.8 kg
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Solution

## The correct option is A 1.2 kg Given: m1=2 kg, u1=u, u2=0, v1=u/4 By conservation of linear momentum m1u1+m2u2=m1v1+m2v2 2u+0=2×u4+m2v2 m2v2=3u2 For elastic collision vseperation=vapproach v2−u4=u ⇒v2=5u4 Now, m2×5u4=3u2 ⇒m2=1.2 kg Alternate Solution: For head on elastic collision we have v1=(m1−m2)u1m1+m2+2m2u2m1+m2 Here m1=2 kg, u1=u, u2=0, v1=u/4 ∴u4=(2−m2)u2+m2⇒m2=1.2 kg Hence option (D) is correct.

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