Physics - Center of Mass Question with Solution | TestHub

The centre of mass of a semicircular wire is at a distance from the circle centre of

$$d=\frac{2R}{\pi }$$

The two semicircles have masses in the ratio

$$m_1:m_2=1:3$$

Their centres of mass are on opposite sides of the circle centre.

$$|y_{\mathrm{CM}}|=\frac{3d-d}{3+1}=\frac{d}{2}=\frac{R}{\pi }$$