A system of three particles having masses `m_(1)=1kg, m_(2)=2kg and m_(3)=4kg` respectively connected by two light springs. The acceleration of the three particles at any instant are 1 `ms^(-2), 2ms^(-2) and 0.5 ms^(-2)` respectively directed as shown in the figure. The net external force acting on the system is

Options

A. 1 N
B. 7 N
C. 3 N
D. 6 N

Answer

C

Explanation

`a_(CM)=F_(eq)/((m_(1)+m_(2)+m_(3)))=(m_(1)a_(1)+m_(2)a_(2)+m_(3)a_(3))/((m_(1)+m_(2)+m_(3)))`
`therefore F_(eq)=m_(1)a_(1)+m_(2)a_(2)+m_(3)a_(3)=1 times 1+2 times 2+4 times (-0.5)=1+4-2=3N`