Question

A thin metalic sheet of mass M is shaped as a square of side L. The moment of inertia about an axis passing through its center is given by ML2/6. What is the moment of inertia with repsect to a parallel axis passing through one of the corners? Enter your answer in terms of M and L.

Answer 1

Answer:

$I = \dfrac{5 ML^2}{12}$

Explanation:

given,

mass of metallic sheet = M

shape of the sheet is square of length L

Moment of inertia When passing through center

                               = $\dfrac{ML^2}{6}$

now, calculating Moment of inertia from one corner

I = Iₓ + MR²

R is the distance is L/2

$I = \dfrac{ML^2}{6} + \dfrac{ML^2}{4}$

$I = \dfrac{2ML^2 + 3 ML^2}{12}$

$I = \dfrac{5 ML^2}{12}$

Moment of inertia through one corner $I = \dfrac{5 ML^2}{12}$