Question

A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be

• A. $\frac{R}{4}$ from the centre
• B. $\frac{R}{3}$ from the centre
• C. $\frac{R}{5}$ from the centre
• D. $\frac{R}{6}$ from the centre

Answer 1

The correct option is D $\frac{R}{6}$ from the centre

Centre of mass of complete disc should lie at point O. $C_1$ is the position of centre of mass of reminaing portion and $C_2$ the position of centre of mass of the removed disc.

$\therefore x$ (Area of remiaing portion ) $=\frac{R}{2}$ (Area of removed disc)
$\therefore x[\pi R^2-\frac{\pi R^2}{4}]=\frac{R}{2}\left[\frac{\pi R^2}{4}\right]$
$\therefore x=\frac{R}{6}$