Find out Co-ordinats of centre of mass of uniform L shaped plate shown in figure. (O is origin)

Options

A. `((5a)/12,(5a)/12)`
B. `((7a)/12,(7a)/12)`
C. `(a/4,a/4)`
D. `(a/3,a/3)`

Answer

A

Explanation

`x_(mc)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`x_(mc)=(m(a/4)+m((3a)/4)+m(a/4))/(3m)`
`x_(cm)=(5a)/12`
Similarly `y_(cm)=(5a)/12`