Two particles of mass 1 kg and 2 kg lie on the same line. If 2kg is displaced 10m rightwards then by what distance 1kg should displaced so that centre of mass will displaced 2m right wards.

Explanation

Initially let us assume that C.O.M is at point C which is` r_(1)` & `r_(2)` distance apart from mass `m_(1)` & `m_(2)` respectively as shown in figure.

from relation `m_(1)r_(1) = m_(2) r_(2)`
`hArr(1)r_(1)=2r_(2)`
Now 2kg is displaced 10 m rightwards then we assume that 1 kg is displaced x m leftward to move the C.O.M 2m rightwards.
So from relation `m_(1)r_(1)'=m_(2)r_(2)'`

`hArr1(x+r_(1)+2)=2(10+r_(2)-2)`
`hArrx+r_(1)+2=10+2r_(2)-4` ...(ii)
from eq. (i) & (ii) x = 14m (leftwards)