Question

A Square Plate of edge d and circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two minutes.

Answer 1

As given in the hint the center of mass of the square plate is supposed to be the $origin.$

And as their areas are in the ratio of $d^2:\pi (d/2{)}^2$

so the ratio of their masses will also be $4:\pi$

if mass of square is $4m$ then that of disc will be $\pi m$

now the x coordinate of center of mass will be $X_{cm}=\frac{4m\times 0+\pi m\times (0.5d+0.5d)}{4m+\pi m}=\frac{\pi d}{4+\pi }$

y coordinate will be $zero$ because the center of mass will be on the line $joining$ the individual center of mass of the

square and circle.