The centre of mass of three bodies each of mass 1 kg located at the points (0,0), (3, 0) and (0, 4) in the x-y plane is

Options

A. `((4)/(3) , 1)`
B. `((1)/(3) , (2)/(3))`
C. `((1)/(2) , (1)/(2))`
D. `(1 , (4)/(3))`

Answer

D

Explanation

Here `m_(1) = 1` kg `(x_(1) , y_(1)) = (0 , 0) ,m_(2) = 1` kg
`(x_(2) , y_(2)) = (3 , 0) ,m_(3) - 1 kg , (x_(3) , y_(3)) = (0,4)`
`X_(CM) = (m_(1) x_(1) + m_(2) x_(2) + m_(3) x_(3))/(m_(1) + m_(2) + m_(3)) = (1 xx 0 + 1 xx 3 + 1 xx 0)/(1 + 1 + 1) = 1`
`Y_(CM) = (m_(1) y_(1) + m_(2) y_(2) + m_(3) y_(3))/(m_(1) + m_(2) + m_(3)) = (1 xx 0 + 1 xx 0 + 1 xx 4)/(1 + 1 + 1) = (4)/(3)`
The coordinates of centre of mass are `(1 , (4)/(3))`