A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the figure. If the center of hole is at a distance c from the center of the disc, the distance `x_(2)` of the center of mass of the remaining part from the initial center of mass O is given by

Options

A. `(pib^(2))/(a^(2) - c^(2))`
B. `(cb^(2))/(a^(2)-b^(2))`
C. `(pic^(2))/(a^(2)-b^(2))`
D. `(ca^(2))/((c^(2)-b^(2)))`

Answer

B

Explanation

Center of mass of whole system was at point O. Hence `x_(2)(pia^(2) - pib^(2)) = c(pib^(2)) rArr x_92) = (cb^(2))/(a^(2)-b^(2))`