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. `hat i(R)/(5) + hat j(R)/(5)`
B. `-hat i(R)/(5) + hat j(R)/(5)`
C. `(-3R)/(14)(hat i + hat j)`
D. None of these

Answer

C

Explanation

( c) If mass of removed disc is `m` then mass of big disc will be `16 m`
`c_(cm) = (16 m(0) - m(0) -m(3 R))/(16 m - m - m) = -(3)/(14) R`
Because of symmetry we can say `y_(cm)` will also have same magnitude
`y_(cm) = -(3)/(14) R`
`vec r_(cm) = -(3)/(14) R (hat i+ hat j)`.