Two balls each of mass 'm' are placed at the vertices A and B of an equilaterial triangle of side 1 m. A third ball of mass 2 m is kept at vertex C. Taking vertex Aas the origin, find the coordinates of the centre-of-mass of the given system.

Options

A. `(1/2m,1/2m)`
B. `(1/2m,sqrt2m)`
C. `(1/2m,sqrt3/4m)`
D. `(sqrt3/4m,sqrt3/4m)`

Answer

C

Explanation

Here centre of mass is given by `barx = (m_1x_1 +m_2 x_2+m_3x_3)/(m_1+m_2+m3) , barx = (mxx0 + m xx1 + 2m xx1//2)/(m+m+2m)`
`bar x = (2m)/(4m) =1/2 , bary = (m_1y_1+m_2y_2+m_3y_3)/(m_1+m_2+m_3)`
`bary=(mxx0+mxx0+2mxxsqrt3//2)/(m+m+2m)=sqrt3/4 " " :.` Centre of mass is `[1/2m,sqrt3/4m]`