Question

A circular plate of diameter d is kept in contact with a square plate of edge d as shown in figure. The densit of the material and the thickness are same
. Everywhere. The centre of mass of the composite system will be
A. Inside the square plate
B. Inside the circular plate
C. At the point of contact
D. Outside the system

Answer 1

Correct Answer - A
(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.