A small disc of radius 2cm is cut from a disc of radius 6cm. If the distance their centers is 3.2cm, what is the shift in the center of mass of the disc?

Options

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

Answer

A

Explanation

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, from original centre.

The position of new centre of mass is given by:
`X_( CM) = (sigma.pib^(2).x_(1))/(sigma.pia^(2)- sigma.pib^(2))`
Here, a = 6 cm, b = 2 cm, `x_(1) = 3.2 cm`
Hence, `X_( CM) = (-sigma xx pi (2)^(2) xx 3.2)/(sigma xx pi xx (6)^(2) - sigma xx pi xx (2)^(2))`
`=(12.8 pi)/(32 pi) = 0.4 cm`