Three masses are placed on the x-axis : 300 g at origin , 500 g at x = 40 cm and 400 g at x = 70 cm . The distance of the centre of mass from the origin is

Options

A. 40 cm
B. 45 cm
C. 50 cm
D. 30 cm

Answer

A

Explanation

The distance of the centre of mass of the system of three masses from the origin O is
`X_(CM) = (m_(1) x_(1) + m_(2) x_(2) + m_(3) x_(3))/(m_(1) + m_(2) + m_(3)) = (300 xx 0 + 500 xx 40 + 400 xx 70)/(300 + 500 + 400)`
`= (500 xx 40 + 400 xx 70)/(1200) = (400 [50 + 70])/(1200)`
` = (50 + 70)/(3) = (120)/(3) = 40` cm