Shown in the figure is a system of three particles having masses `m_(1)=1kg, m_(2)=2kg `and `m_(1)=4kg` respectively connected by two springs. The accelartion of A, B and C at any instant are `1m//sec^(2),2m//sec^(2)` and `1//2m/sec^(2)` respectively directed as shown in the figure. the external force in N acting on the system is. . . ..

Explanation

The acceleration of centrer of mass of the
System `=veca_(cm)=(|m_(1)veca_(1)+m_(2)veca_(2)+m_(3)vca_(3)|)/(m_(1)+m_(2)+m_(3))`
`rArr` The net force acting on the system `= (m_(1)+m_(2)+m_(3))veca_(cm)`
`rArr F_("net")=(m_(1)a_(1)+m_(2)a_(2)-m_(3)a_(3))`
`=[(1)(1)+(2)(2)-(1)/(2)(4)]N=3N`