From the circular disc of radius `4R` two small discs of radius R are cut off. The centre of mass of the new structure will be at

Options

A. (a) `hatiR/5+hatjR/5`
B. (b) `-hatiR/5+hatjR/5`
C. (c) `-hatiR/5-hatjR/5`
D. (d) None of the above

Answer

D

Explanation

`r_(CM)=(A_1r_1-A_2r_2-A_3r_3)/(A_1-A_2-A_3)`
`=(pi(4R^2)(0)-(piR^2)(3Rhati)-(piR^2)(3Rhatj))/(pi(4R)^2-piR^2-piR^2)`
`=(-(3R)/(14)hati-(3R)/(14)hatj)`