Question

What is moment of inertia of a cylinder of radius $r$, along its height ?

• A. $m{r}^2$
• B. $\frac{m{r}^2}{2}$
• C. $\frac{2m{r}^2}{5}$
• D. $\frac{m{r}^2}{5}$

Answer 1

Answer: (B)

To find the moment of inertia of a solid cylinder along its height, we can use the folding method that if we compress the cylinder along its height (central axis), then it is converted into a disc but its mass distribution remains the same about the central axis. Hence its moment of inertia about its height is equal to the moment of inertia of the disc about an axis passing through its centre and perpendicular to its plane.
$\therefore I_{\text{SolidCylinder }}=I_{\text{Disc }}$
$⟹I_{\text{SolidCylinder }}=\frac{1}{2}m{r}^2$