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A uniform thin rod is bent in the form o...

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

Text Solution

Verified by Experts

The correct Answer is:
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)`
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