Find the position of centre of mass of the section shown in figure

Options

A. `(a)/(6),(a)/(6)`
B. `(3a)/2,(3a)/2`
C. `(5a)/6,(5a)/6`
D. a,a,

Answer

C

Explanation

`3/4A_(1)=M,A=4/3 M`
`x_(cm)=(x_(1)m_(1)+x_(2)m_(2))/(m_(1)+m_(2))`
`=(axx(4/3M)+(3a)/2(-M//3))/M`
`=(4a)/3+(-a)/2`
`x_(cm)=a((8-3)/(3xx2))=5/6 a`
Similarly `y_(cm)=5/6 a `