Question

A disc of radius r is placed on a square plate of edge 4r made up of the same sheet with their planes parallel such that any two adjacent sides of square touch the disc

Answer 1

The question is incomplete: we are supposed to find the distance of the center of mass of the system from the center of square plate.

Solution:

Let the masses of disc and squares be x and x' respectively

The center of masses of disc and square are √2 R and √2R

We will assume the center of mass of the system as A from the center of the mass of the square, so,

(x+x') A = (√2R - A) x'

or (x + 2x') A = √2Rx'

or A = √2Rx'/(x+2x')