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. `0.4m`
B. `2.4 cm`
C. `1.8 cm`
D. `1.2 cm`

Explanation

Let radius of complete disc is R and that of similar `R _(1),` Also, let centre of mass now shifts to `o _(2)` is a `x _(2)` from original centre.

The position of new centre of mass is given by
`X _(CM ) = ( - sigma pi b ^(2) x _(1))/( sigma pi a ^(2) - sigma pi b ^(2)), `where `sigma =` mass per unit are
Here ,` a = R = 6 cm, b = R _(1) = 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 . 8pi )/( 32 pi) = - 0. 4 cm`