Three masses of 2 kg, 4 kg and 4 kg are placed at the three points (1, 0, 0), (1, 1, 0) and (0, 1, 0) respectively. The position vector of its centre of massis

Options

A. `(3)/(5) hat(i) + (4)/(5) hat(j)`
B. `(3hat(i) + hat(j))`
C. `(2)/(5) hat(i) + (4)/(5) hat(j)`
D. `(1)/(5) hat(i) + (4)/(5) hat(j)`

Answer

A

Explanation

`x_(CM)= (2 xx 1+ 4 xx 1+ 4 xx 0)/(10) = (3)/(5) (because x_(CM)= (m_(1) x_(1) + m_(2) x_(2) + m_(3) x_(3))/(m_(1) + m_(2) + m_(3)))`
`y_(CM)= (2 xx 0 + 4 xx 1 + 4 xx 1)/(10)= (4)/(5)`
`z_(CM)= 0 and r_(CM)= (3)/(5) hat(i) + (4)/(5) hat(j)`