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

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Question: Answered & Verified by Expert

The moment of inertia of a door of mass

m

, length

2 ℓ

and width

ℓ

about its longer side is

PhysicsRotational MotionJEE Main

Options:

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

Solution:

2988 Upvotes Verified Answer

The correct answer is:

\frac{m ℓ^{2}}{3}

I (about {YY}^{'}) = \frac{m ℓ^{2}}{12}

Using parallel axis theorem :

I (about AD) = \frac{m ℓ^{2}}{12} + \frac{m ℓ^{2}}{4} = \frac{m ℓ^{2}}{3}

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