Question

Two solid hemispheres of radii $R$ and $\frac{R}{2}$ with centers $O$ and $O′$ 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 $OO′$ is $\frac{R}{10}$ find co-ordinates of center of mass of the system.

• A. $\left(- \frac{R}{50} , \frac{21 R}{80}\right)$
• B. $\left(- \frac{R}{30} , \frac{21 R}{80}\right)$
• C. $\left(- \frac{R}{50} , \frac{7 R}{16}\right)$
• D. $\left(- \frac{R}{30} , \frac{7 R}{16}\right)$

Answer 1

Answer: (A)

Let, $M_{2}=M$ , $M_{1}=4M$
$x_{c m}=\frac{4 M \left(O\right) - M \left(\frac{R}{10}\right)}{4 M + M}\Rightarrow x_{cm}=-\frac{R}{50}$
$y_{c m}=\frac{4 M \left(\frac{3 R}{8}\right) - M \left(\frac{R}{16}\right)}{4 M + M}\Rightarrow y_{cm}=\frac{21 R}{80}$