The masses and positions (in rectangular coordinates) of four particles are as follows: 1kg at (a, a), 2kg at `(-a,a)`, 3kg at `(-a,-a)` and 4kg at (a, -a). The position vector of the centre of mass of the system of four particles is

Options

A. `-4 a hat(i)`
B. `-4a hat(i) - 4a hat(j)`
C. 0
D. `-0.4 a hat(j)`

Answer

D

Explanation

Position vector of COM of system is
`r_("COM") = (m_(1) r_(1) + m_(2) r_(2) + m_(3) r_(3) + m_(4) r_(4))/(m_(1) + m_(2) + m_(3) + m_(4))`
`= (1 (a hat(i) + a hat(j)) + 2 (-a hat(i) + a hat(j)) + 3 (-a hat(i) - a hat(j)) + 4(a hat(i) - a hat(j)))/(10)`
`= (0 hat(i) - 4a hat(j))/(10) = - 0.4 a hat(j)`