In the figure shown, find out centre of mass of a system of a uniform circular plate of radius `3R` from O in which a hole of radius R is cut whose centre is at `2R` distance from the centre of large circular plate

Options

A. (a) `R/2`
B. (b) `R/5`
C. (c) `R/4`
D. (d) None of these

Answer

C

Explanation

`x_(CM)=(A_1x_1-A_2x_2)/(A_1-A_2)`
`=(pi(3R)^2(0)-(piR^2)(2R))/(pi(3R)^2-piR^2)=-R/4`
`:.` Distance of centre of mass from origin `=R/4`