Question

From a uniform disc of radius $R$, a circular disc of radius $R/2$ is cut out. The centre of the hole is at $R/2$ from the centre of the original disc. Locate the centre of gravity of the resultant flat body.

• A. $\frac{R}{6}$ from the centre
• B. $\frac{R}{15}$ from the centre
• C. $-\frac{R}{5}$ from the centre
• D. $\frac{R}{20}$ from the centre

Answer 1

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

Let the mass of the disc $=M$

Therefore, the mass of the removed part of disc, $m=\left(M/R^2\right)\ast (R/2{)}^2=M/4$

Now the centre of gravity of the resulting flat body.

$R=[M\ast 0-(M/4)\ast (R/2\left)\right]/(M-M/4)$

$=-\left(MR/8\right)\left(3M/4\right)$

$=-R/6$

Negative sing shown that the centre of gravity lies at positive direction of the original $COM$ at a distance $R/6$.