Two masses A and B of mass M and `2M` respectively are connected by a compressed ideal spring. The system in placed on a horizontal frictionless table and given a velocity `uhat(k)` in the z-direction as shown in the figure. The spring is then released. In the subsequent motion the line from B to A alwyas points along the `hat(i)` unit vector. All some instant of time mass B has a x-component of velocity as `v_(x)hat(i)`. The velocity `vec(v)_(A)` of mass A at that instant is :-

Options

A. `v_(x)hat(i) + uhat(k)`
B. `-v_(x)hat(i) + uhat(k)`
C. `-2v_(x)hat(i) + uhat(k)`
D. `2v_(x)hat(i) + uhat(k)`

Answer

C

Explanation

From `COLM MV_(x_(A)) + 2Mv_(x_(B)) = 0 rArr v_(x_(A)) = -2v_(x_(B))`
so `vec(v)_(A) = -2v_(x)hat(i) + vhat(k)`