Two blocks of mass m and 2m are kept on a smooth horizontal surface. Theya are connected by an ideal spring of force constant k. Initially the spring is unstretched. A constant force is applied to the heavier block in the direction shown in figure. Suppose at time t displacement of smaller block is `x_(1)` then displacement of the heavier block at this moment would be

Options

A. `x/2`
B. `(Ft^(2))/(6m) + x/3`
C. `x/3`
D. `(Ft^(2))/(4m) - x/2`

Answer

D

Explanation

`X_CM = (mx + 2mx_(2m))/(m + 2m)`
`therefore 1/2a_(CM)^(t)^2 = (x+2x_(2m))/3`
`therefore 3/2(F/(3m)t^(2) = x+2x_(2m)`
`therefore X_(2m) = (Ft^(2))/(4m)) - x/2`