Question

The moment of inertia of a door of mass $m$, length $2l$ and width $l$ about its longer side is

• A. $\frac{m{l}^2}{3}$
  
• B. $\frac{5m{l}^2}{24}$
  
• C. $\frac{11m{l}^2}{24}$
  
• D. none of these
  

Answer 1

The correct option is A $\frac{m{l}^2}{3}$


$I\left(\text{about}Y{Y}^{\prime }\right)=\frac{m{l}^2}{12}$

Using parallel axis theorem (about $AD$)

$\frac{m{l}^2}{12}+\frac{m{l}^2}{4}=\frac{m{l}^2}{3}$

Final Answer: $\left(c\right)$