The moment of inertia of a uniform square plate of mass M and edge length a about one of its diagonals is

Question

The moment of inertia of a uniform square plate of mass M and edge length a about one of its diagonals is (A) Ma2 (B) (1/2)Ma2 (C) (Ma2/12) (D) (Ma2/3)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/bbe0e4081f7a15f959e557ce7efbad17-.png" /> lZ = (Ma2/6) By symmetry lx = ly = l lx = ly = lz 2l = (Ma2/6) l = (Ma2/12)

Q. The moment of inertia of a uniform square plate of mass $M$ and edge length a about one of its diagonals is

$M a^{2}$

$\frac{1}{2} M a^{2}$

$\frac{M a ^{2}}{12}$

$\frac{M a ^{2}}{3}$

$l_{Z} = \frac{M a ^{2}}{6}$
By symmetry
$l_{x} = l_{y} = l$
$l_{x} = l_{y} = l_{z}$
$2 l = \frac{M a ^{2}}{6}$
$l = \frac{M a ^{2}}{12}$

Q. The moment of inertia of a uniform square plate of mass M and edge length a about one of its diagonals is

Ma2

21​Ma2

12Ma2​

3Ma2​