A uniform thin rod is bent in the form of closed loop `ABCDEFA` as shown in the figure. The `y-` coordinate of the centre of mass of the system is

Options

A. `(2r)/(pi)`
B. `-(6r)/(3pi+2)`
C. `-(2r)/(pi)`
D. Zero

Answer

B

Explanation

The centre of mass of semicircular ring is at a distance `(2r)/(pi)` from its centre. (Let `lambda =` mass/length)
`therefore Y_(cm)=(lambda pi r xx (2r)/(pi)-lambda xx2pirxx(4r)/(pi))/(lambda pi r+lambdar+lambdar+lambdaxx2pir)=-(6r)/(3pi+2)`