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

`I = (5 ML^2)/(12)`

Step-by-step explanation:

given,

mass of metallic sheet = M

shape of the sheet is square of length L

Moment of inertia When passing through center

=
`(ML^2)/(6)`

now, calculating Moment of inertia from one corner

I = Iₓ + MR²

R is the distance is L/2

`I = (ML^2)/(6) + (ML^2)/(4)`

`I = (2ML^2 + 3 ML^2)/(12)`

`I = (5 ML^2)/(12)`

Moment of inertia through one corner
`I = (5 ML^2)/(12)`