A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of plate as shown. Then center of mass of the combination will be (assume same mass per unit area for the two plates):

Options

A. `(2d)/(2 + pi)` left to the center of the disc
B. `(2d)/(2 + pi)` right to the center of the disc
C. `(4d)/(4 + pi)` right to the center of the disc
D. `(4d)/(4 + pi)` left to the center of the disc

Answer

C

Explanation

`x_(CM) = (0 + lambda d^2 xx d)/(lambda d^2 + lambda pi (d/2)^2)`
`= d/(1 + (pi)/4) = (4d)/(4 + pi) " right to centre of disc".`