The distance between the vertex and the center of mass of a uniform solid planar circular segment of angular size `theta` and radius R is given by -

Options

A. `(4)/(3)R(sin(theta//2))/(theta)`
B. `R(sin(theta//2))/(theta)`
C. `(4)/(3)Rcos((theta)/(2))`
D. `(2)/(3)Rcos(theta)`

Answer

A

Explanation

`X_(CM)=(intdmr(sintheta//2)/(theta//2))/(intdm)[dm=sigmar thetadr]`

`=(2sigmasintheta//2int_(0)^(R)r^(2)dr)/(sigmathetaint_(0)^(R)rdr)implies(4)/(3)R(sin(theta//2))/(theta)`