A body P while moving rectilinearly with velocity $V_{o}$ collides directly with another body Q, which is at rest, as shown below. Assuming both the bodies have the same mass and the collision is elastic, the velocities of the bodies after the collisions, measured positive towards right, are

V_{P} = - V_{o} / 2, V_{Q} = V_{o} / 2

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V_{P} = V_{o} / 2, V_{Q} = V_{o} / 2

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V_{P} = 0, V_{Q} = V_{o} / 2

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V_{P} = 0, V_{Q} = V_{o}

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Solution

The correct option is D $V_{P} = 0, V_{Q} = V_{o}$
For elastic collision e = 1

$V_{Q} - V_{P} = e (u_{p} - u_{q})$

$V_{Q} - V_{P} = V_{O} \Rightarrow V_{Q} = V_{O} + V_{P}$

According to the conservation of linear momentum

$m_{p} u_{p} + m_{q} u_{q} = m_{p} v_{p} + m_{q} v_{q}$

Given

$m_{p} = m_{q} = m, u_{q} = 0, u_{p} = v$

$V_{o} = V_{P} + V_{Q}$

$V_{o} = V_{P} + V_{0} + V_{P}$

$∴ V_{P} = 0$

$∴ V_{Q} = V_{o}$

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