Two semicircular rings of linear densities `lambda` and `2lambda` and of radius `'R'` each are joined to form a complete ring. The distance of the center of the mass 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)`.