Question

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

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

Answer 1

Answer: (C)

$\frac{m{l}^2}{3}$

The integration to calculate Moment of inertia is just similar to that of rod.

${\int }_0^l\frac{m}{l\times 2l}\times 2l\times x^2\times dx={\int }_0^l\frac{m}{l}\times x^2\times dx=\frac{m}{3l}(l^3-0)=\frac{m{l}^2}{3}$