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Question

# A ball of mass 4 kg moving with velocity 4 m/s collides with another identical ball at rest. The kinetic energy of the balls after collision is 78 times of the original. Find the coefficient of restituton (e).

A
1
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B
0.866
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C
0.732
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D
0.239
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Solution

## The correct option is B 0.866 Given: (K.E)final=78(K.E)initial (K.E)loss=(K.E)initial−(K.E)final ⇒(K.E)initial−78(K.E)initial =18(K.E)initial ...(i) We know that (KE)loss=12×m1m2(m1+m2)(uapproach)2(1−e2) ...(ii) Equating (i) and (ii) 12×m1m2(m1+m2)×(uapproach)2(1−e2)=18(K.E.)initial ⇒12×(m×mm+m)×u21×(1−e2)=18(12mu21) ⇒14×(1−e2)=18×12 ⇒e2=1−14=34 or e=√32=0.866

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