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Standard XII

Physics

Velocity of COM

A uniform bar...

Question

A uniform bar of length $6 a$ and mass $8 m$ lies on a smooth horizontal table. Two point masses $m$ and $2 m$ moving in opposite direction in the same horizontal plane with speed $2 v$ and $v$ , respectively. strike the bar and stick to the bar after collision. Calculate.
The velocity of the centre of mass after collision.

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Solution

R.E.F image
conserving momentum of system
Initial momentum = final momentum
$2 m (- V) + m (2 V) + 8 m (0) = (2 m + m + 8 m) V_{e}$
$V_{e} = 0$
after coliseum new com $= \frac{8 m (0) + 2 m (- a) + m (2 a)}{8 m + 2 m + m}$
$= 0$
distance between new com and com of rod $= 0$
$¯ V$ com of rod $= ¯ V$ com of rod about system $+ ¯ V$ com
$= ¯ r \times ¯ w + 0$
(dist b/w com of rod 0 and syst com)
$¯ V$ com of rod $= 0$

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