Question

The uniform solid block shown in figure has mass M and edge dimensions a, b, and c. Calculate its rotational
inertia about an axis passing through one corner and perpendicular to the large faces.​

Answer 1

$\bf\small\bold{\underline{\underline{Step-By-Step\:Explanation:-}}}$

We know that Moment of Inertia of plate passing through 'O' is

Ix = Ma²/12

Iy = Mb²/12

Now by perpendicular axis theorm

Iz = Ma²/12 + Mb²/12

The distance of edge and the center is $\bf\bold{d = \sqrt{(a^2 +b^2)/4} }$

So by parallel axis theorm,

$\bf\bold{I_A= Ma^2/12+ Mb^2/12+Md^2}$

On putting d we get the moment of inertia passing through one corner and perpendicular to the large faces is

$\bf\bold{M(a^2+b^2)/3}$

Note :- source of attachment is Google.

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Brainly Extra Knowledge :

• The ability of body to resist the angular motion is measured in terms of the moment of inertia.