Question

A soild cylinder and a hollow cylinder is having same mass $M$. Hollow cylinder is having the outer radius twice to that of solid cylinder. If $I_s$ and $I_h$ are the moment of inertia about the axis, along the height of the solid cylinder and hollow cylinder respectively passing through their centre, find the ratio of $I_h:I_s$.

• A. $1:1$
• B. $8:1$
• C. $4:1$
• D. $2:1$

Answer 1

The correct option is B $8:1$

Mass of both cylinders $=M$
Let the radius of solid cylinder $=R$
Outer radius of hollow cyclinder $=2R$

The required axis of rotation $Y{Y}^{\prime }$ for both solid cylinder and hollow cylinder is shown in figure given below:

$\text{MI}$ for hollow cylinder,
$I_h=m{r}^2=M(2R{)}^2$
$\therefore I_h=4M{R}^2$
$\Rightarrow$ $\text{MI}$ for solid cylinder,
$I_s=\frac{m{r}^2}{2}=\frac{M{R}^2}{2}$

$\Rightarrow \frac{I_h}{I_s}=\frac{\left(4M{R}^2\right)}{\left(\frac{M{R}^2}{2}\right)}=8$
$\therefore I_h:I_s=8:1$