Question

The moment of inertia of a disc of mass M and radius R about an axis, which is tangential to the circumference of disc and parallel to its diameter, is

• A. $\frac{3}{2}m{R}^2$
• B. $\frac{2}{3}M{R}^2$
• C. $\frac{5}{4}M{R}^2$
• D. $\frac{4}{5}M{R}^2$

Answer 1

The correct option is C

$\frac{5}{4}M{R}^2$

Step-1:Illustrating

From the diagram the moment of inertia about z axis is $I_z=\frac{M{r}^2}{2}$

step-2:finding moment of inertia on Z axis

according to perpendicular axis theorem
moment of inertia about z axis is $$\begin{gathered} I_Z=I_x+I_y \\ {I}_z=2I_x=\frac{M{r}^2}{2} \\ {I}_x=I_y=\frac{M{r}^2}{4} \end{gathered}$$

Step-3:finding moment of inertia about tangential axis

according to the parallel axis theorem, moment of inertia about the tangential axis is

$I_p=I_{COM}+M{x}^2$

$$\begin{gathered} \Rightarrow I_P=\frac{M{r}^2}{4}+M{r}^2 \\ \Rightarrow I_P=\frac{5}{4}M{r}^2 \end{gathered}$$

Hence, option ( c ) is the correct answer.