The velocity (in m/s) of centre of mass of the system as shown in the figure is :

Options

A. `(2 [1 + (4)/(sqrt2)] hat(i) + 8 [(1)/(sqrt2) + 2 ] hat(j))/(7)`
B. `(2 [1 + (4)/(sqrt2)] hat(i) + 8 [(1)/(sqrt2) - 2 ] hat(j))/(7)`
C. `(2 [1 + (4)/(sqrt2)] hat(i) - 8 [(1)/(sqrt2) + 2 ] hat(j))/(7)`
D. `(8 [(1)/(sqrt2) - 2] hat(i) + 2 [1 + (4)/(sqrt2] hat(j)])/(7)`

Answer

C

Explanation

`vec(v)_(COM) = (m_(1) vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3))/(m_(1) + m_(2) + m_(3))`