A circular plate of diameter d is kept in contact with a square plate of edge d as shown in figure. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be
.

Options

A. Inside the square plate
B. Inside the circular plate
C. At the point of contact
D. Outside the system

Answer

A

Explanation

(a) Mass of square plate `M_1 = l^2 sigma`
Mass of circular disc `M_2 = (pi (l^2)/(4)) sigma`
`prop_(cm) =(M_1 xx 0 +(pi l^2 sigma l)/(4))/(l^2 sigma[1 + (pi)/(4)]) rArr x_(cm) = (pi l)/(4 (pi+ 4)/(4)) = (pi l)/(pi + 4)`
`x_(cm) lt (l)/(2)`, i.e., C.O.M. lies in the square.