Two solid hemispheres of radii R and R 2 with centers O and O ′ respectively as shown in figure. The density…

Two solid hemispheres of radii $R$ and $\frac{R}{2}$ with centers $O$ and $O\prime$ respectively as shown in figure. The density of bigger hemisphere is $\rho$ and that of smaller hemisphere is $2\rho$ . Taking center of bigger hemisphere is at origin and the distance between centers of two hemispheres $OO\prime$ is $\frac{R}{10}$ find co-ordinates of center of mass of the system.

1. $\left(-\frac{R}{50},\frac{21R}{80}\right)$
2. $\left(-\frac{R}{30},\frac{21R}{80}\right)$
3. $\left(-\frac{R}{50},\frac{7R}{16}\right)$
4. $\left(-\frac{R}{30},\frac{7R}{16}\right)$

Solution

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