Question

The length of a solid cylinder is $4.5$ times its radius and $I$ is the moment of inertia about its natural axis. This solid cylinder is re-casted into a solid sphere, then the moment of inertia of solid sphere about an axis passing through its centre is :

• A. $\frac{5I}{9}$
• B. $\frac{10I}{9}$
• C. $\frac{9I}{5}$
• D. $\frac{9I}{10}$

Answer 1

The correct option is C $\frac{9I}{5}$

Let $m$ be the mass of the solid cylinder and $r$ be its radius.

So MI about its natural axis is $I=m{r}^2/2$

Height of cylinder $h=4.5r$

When cylinder is recasted into solid sphere, the radius of the solid sphere $R$ is given by $4\pi R^3/3=\pi r^2\times 4.5r\Rightarrow R^3=27r^3/8\Rightarrow R=3r/2$(as volume and mass remains same.)

So MI of solid sphere is $2m{R}^2/5=2m(3r/2{)}^2/5=9m{r}^2/10=9I/5$