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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 kg
Since 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+12mv2
or mv2=15v28 (ii)
Using (i) in (ii) we get m = 1.2 kg. Hence the correct choice is (b).

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