Question

A circular plate of uniform thickness has a diameter of 28 cm. A circular portion of diameter 21 cm is removed from the plate as shown. Origin is the center of mass of complete plate. The position of center of remaining portion will shift toward left from origin by :

• A. 5 cm
• B. 9 cm
• C. 4.5 cm
• D. 5.5 cm

Answer 1

The correct option is C 4.5 cm

$Y_{CM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$0=\frac{\rho \pi (10.5{)}^{2}t\times 3.5+\rho \pi ({14}^2-{10.5}^2)t{x}_2}{m_1+m_2}$

Here $\pi r^{2}t$ is volume and mass is written in terms of density times volume, where $\rho$ is the density of plate material and $t$ is the thickness of the plate.

$x_2=\frac{{10.5}^2\times 3.5}{{14}^2-{10.5}^2}$

$x_2=4.5cm$