A circular plate of diameter ' a ' is kept in contact with a squa… - Vidyadip

MCQ

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
✓
Inside the square plate
C
At the point of contact
D
Outside the system

✓

Answer

Correct option: B.

Inside the square plate

b
(b)

$x_{c m}=\frac{A_1 x_1+A_2 x_2}{A_1+A_2} \quad$ [ taking origin at contact point ]

$=\frac{\frac{\pi a^2}{4}\left(\frac{-a}{2}\right)+a^2\left(\frac{a}{2}\right)}{\frac{\pi a^2}{4}+a^2}=\frac{a^3\left(1-\frac{\pi}{4}\right)}{2 a^2\left(a+\frac{\pi}{4}\right)}$

$=\frac{a\left(1-\frac{\pi}{4}\right)}{2\left(1+\frac{\pi}{4}\right)} > 0$

$\Rightarrow x_{c m}$ is inside the square plate

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