Shown in the figure is a system of three particles of mass `1 kg, 2 kg` and `4 kg` connected by two springs. The acceleration of `A. B` and `C` at any instant are `1 ms^(-2), 2 ms^(-2)` and `1//2 ms^(-2)` respectively directed as shown in the figure external force acting on the system is

Options

A. `1N`
B. `7N`
C. `3N`
D. none of these

Answer

C

Explanation

The aceeleration of centre of mass of the system
`a_(cm)=(|m_(1)veca_(1)=vecm_(2)a_(2)+m_(3)veca_(3)|)/(m_(1)+m_(2)+m_(3))`
`implies` the net force acting of the system
`=|m_(1)veca_(1)+vecm_(2)a_(2)+m_(3)veca_(3)|`
`implies F_(net)=(m_(1)a_(1)+m_(2)a_(2)-m_(3)a_(3))`
`=[(1)(1)+(2)(2)-1/2(4)]N=3N`