A square plate and a circular plate made up of same material are placed touching each other on a horizontal table. If the side length of square plate is equal to diameter of the circular plate then the centre of mass of the system will be:

If $\sigma$ be the surface density of mass of the square and circular plates , then

$m_1$ =Mass of the sqaure = $a^2\sigma$ .

$m_2$ = Mass of the circular plate = π$a^2\sigma$

$m_1$  > $m_2$

The square plate and the circular plate can be replaced by two particles of mass m1 and m2 respectively.

$r_1$  = Distance of COm from ${\mathrm{m}}_1$ = $\frac{{\mathrm{m}}_2\mathrm{a}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

$r_2$ = Distance of COM from ${\mathrm{m}}_2$ = $\frac{{\mathrm{m}}_1\mathrm{a}}{{\mathrm{m}}_1+{\mathrm{m}}_2}$

 $r_1$ < $r_2$ and $r_1$ < $\frac{\mathrm{a}}{2}.$