Question

A circular plate of diameter ' $a$ ' is kept in contact with a square plate of side a as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be

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

Answer 1

Answer: (B)

$x_{c m}=\frac{A_{1} x_{1}+A_{2} x_{2}}{A_{1}+A_{2}}$ [taking origin at contact point]
$=\frac{\frac{\pi a^{2}}{4}\left(\frac{-a}{2}\right)+a^{2}\left(\frac{a}{2}\right)}{\frac{\pi a^{2}}{4}+a^{2}}=\frac{a^{3}\left(1-\frac{\pi}{4}\right)}{2 a^{2}\left(a+\frac{\pi}{4}\right)}$
$=\frac{a\left(1-\frac{\pi}{4}\right)}{2\left(1+\frac{\pi}{4}\right)} > 0$
$\Rightarrow x_{cm}$ is inside the square plate