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Two particles of mass 1 kg and 0.5 kg ar...

Two particles of mass 1 kg and 0.5 kg are moving in the same direction with speed of `2 m//s` and 6 m/s respectively on a smooth horizontal surface. The speed of centre of mass of the system is

Text Solution

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Velocity of c.m. of the system is given as
`vec(v)_(cm)=(m_(1)vec(v)_(1)+m_(2)vec(v)_(2))/(m_(1)+m_(2))`
Since the particles `m_(1)` & `m_(2)` are moving unidirectionally,
`m_(1)vec(v)_(1)` and `m_(2)vec(v)_(2)` are parallel.
`rArr |m_(1)vec(v)_(1)+m_(2)vec(v)_(2)|=m_(1)v_(1)+m_(2)v_(2)`
Therefore,
`v_(cm)=(|m_(1)vec(v)_(1)+m_(2)vec(v)_(2)|)/(m_(1)+m_(2))=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))=((1)(2)+(1//2)(6))/((1+(1)/(2)))m//s=3.33` m/sec.
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