Question

The moment of inertia of a solid cylinder about an axis parallel to its length and passing through its centre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is:

• A. $1:\sqrt{2}$
• B. $1:2$
• C. $1:\sqrt{3}$
• D. $1:3$

Answer 1

Answer: (C)

$1:\sqrt{3}$

The moment of inertia of a solid cylinder about an axis parallel to its length and passing through its center is $I_1=\frac{m{r}^2}{2}$

moment of inertia about an axis perpendicular to the length of cylinder and passing through its center $I_2=\frac{m{r}^2}{4}+\frac{m{l}^2}{12}$

Now $I_1=I_2\Rightarrow \frac{r}{l}=1:\sqrt{3}$