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Question

# A 4 kg ball moving to the right at 6 m/s collides with a 5 kg ball ahead of it and moving to the right at speed 2 m/s . Find the magnitude of final velocity of the 4 kg and 5 kg balls respectively, if coefficient of restitution is 0.5.

A
4.4 m/s, 3.4 m/s
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B
2.66 m/s, 4.66 m/s
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C
3.33 m/s, 5.33 m/s
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D
5 m/s, 7 m/s
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Solution

## The correct option is B 2.66 m/s, 4.66 m/sLet m1=4 kg, m2=5 kg Applying conservation of momention before and after collision: Applying PCLA on the system of two balls, m1u1+m2u2=m1v1+m2v2 or, (4×6)+(5×2)=4v1+5v2 ∴4v1+5v2=34 ...(i) For coefficient of restitution (e), e=Speed of separationSpeed of approach or 0.5=v2−v16−2 ⇒v2−v1=0.5×4=2 ...(ii) Multiplying by 4 in Eq. (ii) and adding to Eq (i), ⇒9v2=34+8=42 ∴v2=429=4.66 m/s Putting in Eq (ii), v1=v2−2 ∴v1=2.66 m/s

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