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Question

A ball collides elastically with another ball of the same mass. The collision is oblique and initially second ball was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocities of the balls after the collision?


A

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B

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C

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D

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Solution

The correct option is D


Applying law of conservation of momentum along direction of initial velocity we get

mu=mv(cos θ1+cos θ2)

Applying law of conservation of momentum perpendicular to direction of initial velocity

0=mv sin θ1mv sin θ2θ1=θ2mu=2 mv cos θ [θ1=θ2=θ]cos θ=u2v (ii)

According to law of conservation of KE,

12mu2=12mv2+12mv2u2=2v2 or u=2v (iii) From Eqs. (ii) and (iii), we have cos θ=2v2v

or cos θ=12 or θ=45θ1+θ2=90


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