An equilateral triangular plate of mass `4m` of side a is kept as shown. Consider two cases: (i) a point mass `4m` is placed at the vertex P of the plate (ii) a point mass `m` is placed at the vertex R of the plate. In both cases the x-coordinate of centre of mass remains the same. Then x coordinate of centre of mass of the plate is

Options

A. (a) `a/3`
B. (b) `a/6`
C. (c) `(6a)/(7)`
D. (d) `(2a)/(3)`

Answer

B

Explanation

`((4m)X_1+(4m)(a/2))/(8m)=((4m)X_1+(m)(a))/(5m)`
Solving this equaiton, we get
`X_1=X`-coordinate of COM of plate
`=a/6`