Question

Four solid rigid balls each of mass $m$ and radius $r$ are fixed on a rigid-ring of radius $2r$ and mass $2m$. The system is whirled about ${}^{\prime }{O}^{\prime }$ as shown. The radius of gyration of the system is $128m{r}^2/30.$ how$?$

• A. $r\sqrt{\frac{128}{5}}$
• B. $r\sqrt{\frac{88}{5}}$
• C. $r\sqrt{\frac{128}{30}}$
• D. $r\sqrt{\frac{88}{30}}$

Answer 1

The correct option is B $r\sqrt{\frac{88}{5}}$

about $O$

$M.I.$ of ring $=2m{\left(2r\right)}^2$

$M.I.$ of a ball $=2m{r}^2/5+m{\left(2r\right)}^2=22m{r}^2$

So total $=8m{r}^2+4\times 22m{r}^2/5=r\sqrt{\frac{88}{5}}$

Hence,

option $\left(B\right)$ is correct answer.