Question

If the density of material of a square plate and a circular plate shown in is same, the centre of mass of the composite system will be

• A. Inside the square plate
• B. Inside the circular plate
• C. At the point of contact
• D. Outside the system

Answer 1

Answer: (A)

Mass of square plate $M_1={\ell }^2\sigma$
Mass of circular disc $M_2=\left(\pi \frac{{\ell }^2}{4}\right)\sigma$

${\alpha }_{cm}=\frac{M_1\times 0+\frac{\pi {\ell }^2\sigma \ell }{4}}{{\ell }^2\sigma \left[1+\frac{\pi }{4}\right]}$
$\Rightarrow x_{cm}=\frac{\pi \ell }{4\frac{(\pi +4)}{4}}=\frac{\pi \ell }{\pi +4}$
$x_{cm}<\frac{\ell }{2}$, i.e., C.O.M. lies in the square