A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance aR from the centre of the bigger disc. The value of a is

Options

A. `1/2`
B. `1/3`
C. `1/4`
D. `1/6`

Answer

B

Explanation

Mass of cut portion,` m = (pi R^(2)M)/(pi(2R)6(2))=M/4`
As new centre of mass is at, `e_(1)=R`
`X_(CM)= alpha R=(Mxx 0- [M/4]xxR)/(M-[M/4])=-R/3`
alpha=-1/3
[Negative sign only indicates, opposite direction]