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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)initial78(K.E)initial
=18(K.E)initial ...(i)

We know that
(KE)loss=12×m1m2(m1+m2)(uapproach)2(1e2) ...(ii)
Equating (i) and (ii)
12×m1m2(m1+m2)×(uapproach)2(1e2)=18(K.E.)initial
12×(m×mm+m)×u21×(1e2)=18(12mu21)
14×(1e2)=18×12
e2=114=34
or e=32=0.866

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