A uniform metal dise of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of the mass of the remaining part will be:

Options

A. `R/4` from the centre
B. `R/3` from the centre
C. `R/5` from the centre
D. `R/6` from the centre

Answer

D

Explanation

Centre of mass of complete disc should lie at point O. `C_(1)` is the position of centre of mass of mass of remaining portion and `C_(2)` the position of centre of mass of the removed disc.
`:.` x (Area of remaining portion) `=R/2` (Area of removed disc)

`:. x[pi R^(2) - (pi R^(2))/4]=R/2[(pi R^(2))/4]`
`:. x=R/6`