Three point masses `m_(1), m_(2) and m_(3)` are placed at the corners of a thin massless rectangular sheet `1.2m xx 1m)` as shown. Center of mass will be located at the point.

Options

A. (0.8,0.6)m
B. (0.6, 0.8)m
C. (0.4, 0.4)m
D. (0.5, 0.6)m

Answer

C

Explanation

`m_(1) = 1.6 kg, (x_(1),y_(1)) = (0,0)`
`m_(2) = 2kg, (x_(2),y_(2)) = (1.2,0)`
`m-93) = 2.4 kg, (x_(3),y_(3)) = (0,1)`
`therefore` Coordinates of center of mass will be
`x_(CM) = (m_(1)x_(1) +m_(2)x_(2) + m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`((1.6)(0) + (2)(1.2)+(2.4)(0))/(1.6 + 2 + 2.4)`
`x_(CM) = 0.4m`
`y_(CM) = ((m_(1)y_(1) + m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))`
`=((1.6)(0)+(2)(0) + (2.4)(1))/(1.6 + 2+2.4)`
`y_(CM) = 0.4`m
`therefore Coordiantes of center of mass = (0.4,0.4)m