Question

A uniform square plate and a disc having same mass per unit area are kept in contact as shown in figure. Locate the position of the centre of mass of the system w.r.t. centre of the square. [Diameter of the disc = Side length of square plate = a]

Answer 1

Let mass of square plate be $M$ & mass of disc be $m$

$\frac{M}{a^2}=\frac{m}{\frac{T{a}^2}{4}}=K$

$M=K{a}^2$

$m=\frac{\pi K{a}^2}{4}$

w.r.t centre of square

$X_{cm}=\frac{M\left(o\right)+m\left(a\right)}{M+m}$

$=\frac{\left(\frac{\pi K{a}^2}{4}\right)a}{a^2(K+\frac{\pi K}{4})}$

$=\frac{\pi Ka}{4K+\pi K}$

$=\frac{\pi a}{4+\pi }$
$Y_{cm}=0$