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Question

A ball of mass 10 kg is moving with a velocity of 10 m/s. It strikes another ball of mass 5 kg, which is moving in the same direction with a velocity of 4 m/s. If the collision is elastic, their respective velocities after the collision will be

A
12 m/s,6 m/s
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B
12 m/s,25 m/s
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C
6 m/s,12 m/s
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D
8 m/s,20 m/s
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Solution

The correct option is C 6 m/s,12 m/s
Let their velocities after the collision be v1 and v2. As we know for elastic collision, relative velocity of approach = relative velocity of separation
104=v2v16=v2v1
v1=v26
Applying conservation of momentum,
10×10+5×4=10v1+5v2
120=10v1+5v2
120=10(v26)+5v2=15v260
15v2=180v2=12 m/s,
v1=6 m/s
v2=12 m/s

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