Figure shows a square lamina with a disc of radius `L/2` removed from it which is now placed symmetrically over upper right quarter what is location of centre of mass of system relative to origin shown in figure

Options

A. `(piL)/12(hat(i)+hat(j))`
B. `(piL)/8(hat(i)+hat(j))`
C. `(piL)/4(hat(i)+hat(j))`
D. `(piL)/16(hat(i)+hat(j))`

Answer

D

Explanation

`X_(Cr)=(((pim)/16)L/sqrt(2)-(pim)/16(-L/sqrt(2))+m)/m`
`Rightarrow pi/8(L/sqrt(2))from origin`
` vec(r) = pi/8(L/sqrt(2)) (cos45hat(i)+son45hat(j))=(piL)/8(hat(i)+hat(j))`
`=+(ml)/m=+(sigmapiL^(2))/(4sigmaL^(2)) L=pi/4L`