Question

A square plate of edge ${}^{\prime }{a}^{\prime }$ and a circular disc of same diameter are placed touching each other at the midpoint of an edge of the plate as shown in figure. If mass per unit area for the two plates are same then find the distance of center of mass of the system from the centre of the disc.

Answer 1

Let $\sigma$ is mass per unit area of both plates and consider origon as a center of disc.

Let the centre of mass of the system from the centre of the disc$=x$,

$x=\frac{m_1\times x_1+m_2\times x_2}{m_1+m_2}$

$\Rightarrow x=\frac{\sigma \times \pi \frac{a^2}{4}\times 0+\sigma a^2\times a}{\sigma \pi \frac{a^2}{4}+\sigma \times a^2}=\frac{4a}{\pi +4}$