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Question

Two equal spheres of mass m are in contact on a smooth horizontal table. A third identical sphere impinges symmetrically on them and is reduced to rest. Find the loss of K.E


A

15mu2

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B

16mu2

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C

23mu2

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D

35mu2

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Solution

The correct option is B

16mu2


Let u = velocity of sphere A before impact. As the sphere are identical, the triangle ABC formed by joining their centres is equilateral. The spheres B & C will move in direction AB and AC after impact making an angle of 30 with the original lines of motion of ball A.

Let v = speed of the other balls after impact

Momentum Conservation:

mu = mv cos 30 + mv cos 30

u = v3 ........(i)

for an oblique collision, we have to take components along normal i.e., along AB for balls A and B

vBvA = e(uBuA) v0 = e(0u cos 30)

v = eucos 30

combining (i) and (ii), we get e = 23.

Loss in KE = 12mu22(12mv2) = 12mu2m(u3)2 = 16mu2


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