Question

# A ball P of mass 2 kg undergoes an elastic collision with another ball Q initially kept at rest. After the collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q?

A
0.9 kg
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B
1.2 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 B 1.2 kgSince the collision is elastic, both momentum and kinetic energy are conserved. If m is mass of ball Q and v’ its speed after the collision, the law of conservation of momentum gives 2v=2×v4+mv′ Where v is the original speed of ball P. thus mv′=3v2 or v′=3v2m (i) The law of conservation of energy gives 12×2×v2=12×2×(v4)2+12mv′2 or mv′2=15v28 (ii) Using (i) in (ii) we get m = 1.2 kg. Hence the correct choice is (b).

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