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 :

Options

A. `(3R)/(8 pi)`
B. `(2R)/(3 pi)`
C. `(3R)/(4 pi)`
D. None of these

Answer

B

Explanation

Let the two half rings be placed in left and right of y-axis centre as shown in the figure.

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