The velcoity of centre of mass of the system as shown in the figure :-

Options

A. `((2 - 2sqrt3)/(3)) hat(i) - (1)/(3)hat(j)`
B. `((2 + 2sqrt3)/(3)) hat(i) - (2)/(3) hat(j)`
C. `4 hat(i)`
D. None of these

Answer

B

Explanation

`vec(v)_(cm) = (m_(1)vec(v)_(1) + m_(2)vec(v)_(2))/(m_(1) + m_(2)) = (1 xx 2hat(i) + 2 xx (2 cos30hat(i) - 2sin 30hat(j)))/(3)`
`= ((2 + 2sqrt3)/(3))hat(i) - (2)/(3)hat(j)`