Question

Moment of inertia of a disc about the tangent parallel to its plane is $I$. The moment of inertia of the disc tangent and perpendicular to its plane is

• A. $\frac{3I}{4}$
  
• B. $\frac{3I}{2}$
  
• C. $\frac{5I}{6}$
  
• D. $\frac{6I}{5}$
  

Answer 1

The correct option is D $\frac{6I}{5}$

We know that the Moment of inertia of a disc about the center and parallel to its plane is $\frac{M{R}^2}{4}$

So using parallel axis theorem, Moment of inertia of a disc about the tangent parallel to its plane is $\frac{M{R}^2}{4}+M{R}^2=\frac{5M{R}^2}{4}=I$

Now, using perpendicular axis theorem the moment of inertia of the disc tangent and perpendicular to its plane is $\frac{5M{R}^2}{4}+\frac{M{R}^2}{4}=\frac{6M{R}^2}{4}=\left(\frac{6}{5}\right)\frac{5M{R}^2}{4}=\frac{6I}{5}$

Therefore, D is the correct option.