Question

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

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

Answer 1

Correct Answer - B
The centre of mass of semicircular ring is at a distance `(2r)/(pir) ` from its centre. `(` Let `lambda=` mass `//` length `)`
`:. Y_(cm)=(lambdapirxx(2r)/(pi)-lambda xx 2pirxx(4r)/(pi))/(lambda pir+lambdar+lambdar+lambda xx 2pir)=-(6r)/(3pi+2)`