A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumference of the discs coincoid . The centre of mass of the new disc is `alphaR` from the centre of the bigger disc . the value of `alpha ` is

Options

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

Answer

A

Explanation

Mass of original disc = m
Mass of disc removed, `m_(1) = m/4`
Mass of remaining disc `=(3m)/4`
Mass `m_(1)` and `m_(2)` are concentrated at `O_(1)` and `O_(2)` respectively and O is their centre of mass.
Moment of `m_(1)` about O = moment of `m_(2)` about O.
`m/4 xx R = (3m)/R xx alpha R rArr alpha =1/3`