Particles of mass 2 kg, 2 kg, 1 kg and 1 kg are placed at the corners A, B, C and D of a square of side L as shown in figure. Locate the centre of mass of the system.

Options

A. `L/3, L/2`
B. `L/2, L/3`
C. L, L
D. None of these

Answer

B

Explanation

If A is taken as origin,
Then, `X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))=(2 times 0+2 times L+1 times L+1 times 0)/6=1/2L`
`Y_(CM)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))=(2 times 0+2 times 0+1 times L+1 times L)/6=1/3L`