A system consists of 3 particles each of mass m located at points (1, 1), (2, 2) and (3, 3). The coordinates of the centre of mass are

Options

A. (6,6)
B. (3,3)
C. (1 ,1)
D. (2 ,2)

Answer

D

Explanation

The coordinates of the centre of mass are
`X_(CM) = (m_(1) x_(1) + m_(2) x_(2) + m_(3) x_(3))/(m_(1) + m_(2) + m_(3)) = (m xx 1 + m xx 2 + m xx 3)/(m + m + m)`
`Y_(CM) = (m_(1) y_(1) + m_(2) y_(2) + m_(3) y_(3))/(m_(1) + m_(2) + m_(3)) = ( m xx 1 + m xx 2 + m xx3)/(m + m + m) = 2`
Hence , the coordinates of centre of mass are (2,2)