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 m ℓ2/24) (B) (5 m ℓ2/24) (C) (m ℓ2/3) (D) None of these

Tardigrade Admin · Accepted Answer

I about Y prime=( m ℓ2/12) Using parallel axis theorem: I( text about AD )=( m ℓ2/12)+( m ℓ2/4)=( m ℓ2/3) <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-cap7rnqpkfpeq4rv.jpg" />

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

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

2411mℓ2​

245mℓ2​

3mℓ2​