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

Question

The moment of inertia of a door of mass m, length 2 l and width l about its longer side is (A) (11 ml 2/24) (B) (5 ml 2/24) (C) (m l2/3) (D) none of these

Tardigrade Admin · Accepted Answer

I(. about .Y Y prime)=(m l2/12) Using parallel axis theorem: (about AD) (m l2/12)+(m l2/4)=(m l2/3)

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

$\frac{11 m l ^{2}}{24}$

$\frac{5 m l ^{2}}{24}$

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

none of these

$I ($ about $Y Y^{'}) = \frac{m l ^{2}}{12}$
Using parallel axis theorem:
(about AD) $\frac{m l ^{2}}{12} + \frac{m l ^{2}}{4} = \frac{m l ^{2}}{3}$

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

2411ml2​

245ml2​

3ml2​