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Question

In the figure shown below, two identical balls of mass M and radius R each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass M and radius R/2, is coming down vertically and has a velocity v0 when it hits the two balls symmetrically and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to


A
4v03
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B
2v03
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C
v03
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D
3v0
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Solution

The correct option is C v03
Assuming that the impulse imparted to each ball on the surface, during the collision is J. Since the situation is symmetric, the two balls on the ground will move with the same velocity.


For ball B:

Jcosθ=Mv ......(1)

And for ball C:

2Jsinθ=0Mv0

2Jsinθ=Mv0 .......(2)

From Eqs.(1) and (2),

tanθ=v02v .........(3)

From ΔAOC,

OC=AC2AO2=94R2R2=52R

tanθ=OCAO=5R/2R=52

From equation (3),

52=v02vv=v05

Hence, option (C) is correct.

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