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)

$x_{cm}=\frac{A_1{x}_1+A_2{x}_2}{A_1+A_2}$ [taking origin at contact point]
$=\frac{\frac{\pi a^2}{4}\left(\frac{-a}{2}\right)+a^2\left(\frac{a}{2}\right)}{\frac{\pi a^2}{4}+a^2}=\frac{a^3\left(1-\frac{\pi }{4}\right)}{2a^2\left(a+\frac{\pi }{4}\right)}$
$=\frac{a\left(1-\frac{\pi }{4}\right)}{2\left(1+\frac{\pi }{4}\right)}>0$
$\Rightarrow x_{cm}$ is inside the square plate