Question

In the figure shown, find out the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from $O$. On this plate, a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of the plate.

• A. $\frac{R}{4}$
• B. $\frac{R}{5}$
• C. $\frac{R}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{R}{4}$

From law of conservation of center of mass,
$\overline{x}=\frac{m_1{x}_1+(-m_2)x_2}{m_1+(-m_2)}$
$=\frac{A_1{x}_1+(-A_2)x_2}{A_1+(-A_2)}$
Again, $A_1=\pi {\left(3R\right)}^2$,
$A_2=\pi R^2$
Solving, $x_1=0$,
$x_2=2R$
$\therefore \overline{x}=-R/4$