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The distance between the vertex and the ...

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 -

A

`(4)/(3) R(sin (theta//2))/(theta)`

B

`R (sin (theta//2))/(theta)`

C

`(4)/(3)R cos ((theta)/(2))`

D

`(2)/(3) R cos (theta)`

Text Solution

Verified by Experts

The correct Answer is:
A
`X_(CM)= (int dmr (sin theta//2)/(theta//2))/(int dm) [dm= sigma r theta d r]`
`=(2 sigma sin theta//2 int_(0)^(R) r^(2) dr)/(sigma theta int_(0)^(R)r dr) rArr (4)/(3) R (sin (theta//2))/(theta)`
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