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Two semicircular rings of linear mass de...

Two semicircular rings of linear mass densities `lamda` and `2 lamda` and of radius 'R' each are joined to form a complete ring. The distance of the centre of the mass of complete ring from its geometrical centre is :

A

`(3R)/(8pi)`

B

`(2R)/(3pi)`

C

`(3R)/(4pi)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let the two half rings be placed in left and right of `y-` axis with centre centre as shown in figure.

Then the coordinate of centre of mass of left and right half rings are `(-(2R)/(pi),0) ` and `((2R)/(pi),0)`
`:. x-` coordinates of centre of mass of comple ring is
`(m(-(2R)/(pi))+2m((2R)/(pi)))/(3m)=(2R)/(3pi)`
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