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Standard XII

Physics

Collision Examples I

Three particl...

Question

Three particles each of mass m are located at vertices of an equilateral triangle ABC. They starts moving with equal speed v each along the medians of the triangle and collide at its centroid G. If, after collision, A comes to rest and B retraces its path along GB, then C

also comes to rest.

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moves with a speed v along CG.

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moves with a speed v along BG.

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moves with a speed v along AG.

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Solution

The correct option is B moves with a speed v along BG.
Since $F_{e x t} = 0$ , momentum will be conserved.
$m (v_{A G} + v_{B G} + v_{C G}) = m (v_{1}^{'} + v_{2}^{'} + v_{3}^{'}) = m (0 + v_{G B} + v_{3}^{'})$
Since initial momentum is zero,
$v_{G B} + v_{3}^{'} = 0$
$\Rightarrow v_{3}^{'} = - v_{G B} = v_{B G}$
Thus C moves with a speed v along BG.
Hence, C will moves with a speed v along BG.

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Three particles each of mass m are located at vertices of an equilateral triangle ABC. They starts moving with equal speed v each along the medians of the triangle and collide at its centroid G. If, after collision, A comes to rest and B retraces its path along GB, then C

The correct option is B moves with a speed v along BG.Since Fext=0, momentum will be conserved.m(vAG+vBG+vCG)=m(v′1+v′2+v′3)=m(0+vGB+v′3)Since initial momentum is zero, vGB+v′3=0⇒v′3=−vGB=vBGThus C moves with a speed v along BG.Hence, C will moves with a speed v along BG.