Find out the position of centre of mass of the figure shown below.

Explanation

We divide the above problem in two parts
(i) First find out position of centre of mass of both semicircular plate and rectangular plate separately.
(ii) Then find the position of centre of mass of given structure .
Centre of mass of semicircular disc lie at `(4R)/(3pi)`
`hArrAB=(4R)/(3pi)`
Centre of mass of rectangular plate lie at the centre of plate at point C
`hArrBC C=R`

`m_(SC)=(sigmapiR^(2))/2` , `m_(R)=sigma4R^(2)`

`rArrLet us assume COM is at `r_(1)` distance from `m_(R)`
`rArrr_(1)=(sigma.(piR^(2))/2(R+(4R)/(3pi)))/(sigma.(piR^(2))/2+sigma4R^(2))`
`rArrr_(1)=(piR(3pi+4))/(3(pi+8))`