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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 = v√3 ........(i) for an oblique collision, we have to take components along normal i.e., along AB for balls A and B vB−vA = −e(uB−uA) ⇒ v−0 = −e(0−u cos 30∘) v = eucos 30∘ combining (i) and (ii), we get e = 23. Loss in KE = 12mu2−2(12mv2) = 12mu2−m(u√3)2 = 16mu2

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