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 $M_{2}=\left(\pi \frac{\ell^{2}}{4}\right) \sigma$

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