Question

A small disc of radius $2cm$ is cut from a disc of radius $6$ cin. If the distance between their centres is $3.2cm$, what is the shift in the centre of mass of the disc?

• A. 0.4 cm
• B. 2.4 cm
• C. 1.8 cm
• D. 1.2 cm

Answer 1

Answer: (A)

The situation can be shown as :
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, $a=6cm,b=2cm,x_1=3.2cm$
Hence, $X_{CM}=\frac{-\sigma \times \pi (2{)}^2\times 3.2}{\sigma \times \pi \times (6{)}^2-\sigma \times \pi \times (2{)}^2}$
$=\frac{12.8\pi }{32\pi }$
$=-0.4cm$