Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:

Question

Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by: (A) ( M l2/6) (B) M l2 (C) ( M l2/12) (D) (2/3) M l2

Tardigrade Admin · Accepted Answer

According to perpendicular Axis theorem. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b973d7292c5030be9bf7064b11fe377b-.png" /> I x + I y = I z I z ⇒ ( m ℓ2/3)+( m ℓ2/3) =(2 m ℓ2/3)

Q. Moment of inertia of a square plate of side $l$ about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:

$\frac{M l ^{2}}{6}$

$M l^{2}$

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

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

According to perpendicular Axis theorem.

$I_{x} + I_{y} = I_{z}$
$I_{z}$
$\Rightarrow \frac{m ℓ ^{2}}{3} + \frac{m ℓ ^{2}}{3}$
$= \frac{2 m ℓ ^{2}}{3}$

Q. Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by:

6Ml2​

Ml2

12Ml2​

32​Ml2