Question

A small disc of radius $2\,cm$ is cut from a disc of radius $6\,cm.$ Distance between centres of disc is $3.2\,cm.$ Find the distance of center of mass of remaining disc from center of original disc.

• A. $0.4\,cm$
• B. $2.4\,cm$
• C. $1.8\,cm$
• D. $1.2\,cm$

Answer 1

Answer: (A)

Let radius of complete disc is a and that of small disc is $b$ also let centre of mass now shifts to $O_{2}$ at a distance $x_{2}$ from original centre.

The position of new centre of mass is given by
$X_{CM}=\frac{\sigma \cdot \pi b^{2} \cdot x_{1}}{\sigma \cdot \pi a^{2} - \sigma \cdot \pi b^{2}}$
Here, $a=6\,cm,b=2\,cm,x_{1}=3.2\,cm$
Hence, $X_{CM}=\frac{- \sigma \times \pi \left( 2^{2} \times 3 . 2\right)}{\sigma \times \pi \times \left( 6^{2} - \sigma \times \pi \times 2^{2}\right)}{ }$
$=\frac{12 . 8 \pi }{32 \pi }=0.4cm$