Question

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its center of mass and perpendicular to length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

• A. $I_0+2M{L}^2$
  
• B. $I_0+M{L}^2$
  
• C. $I_0+\frac{M{L}^2}{4}$
  
• D. $I_0+\frac{M{L}^2}{2}$
  

Answer 1

The correct option is C $I_0+\frac{M{L}^2}{4}$


$I_{end}=I_{cm}+M{d}^2=I_0+M{\left(\frac{L}{2}\right)}^2=I_0+\frac{M{L}^2}{4}$
Final Answer: $\left(c\right)$