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Two particles of masses 1kg and 2kg are ...

Two particles of masses 1kg and 2kg are located at `x=0` and `x=3m`. Find the position of their centre of mass.

Text Solution

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Since both the particles lie on x-axis, the COM will also lie on x-axis. Let the COM is located at `x=x`, then
`r_(1)=`distance of COM from the particle of mass `1 kg=x`
and `r_(2)=`distance of COM from the particle of mass 2 kg
`=(3-x)`
we know
`x_(c)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+m_(2))`
Given, `x_(1)=0,x_(2)=3`
`m_(1)=1kg,m_(2)=2kg`
`x_(c)=(1xx0+2xx3)/(1+2)`
`x=2m`
As expected, the centre of mass is nearer to the heavier mass.
using `m_(1)r_(1c)+m_(2)r_(2c)=0`
`m_(1)(0-x)+m(3-c)=0`
`-x+6-2x=0`
Or `x=2m`
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