Moment of inertia of a square plate of mass 'm' and side 'a' about the given axis is equal to (axis is in the plane of the plate and passing through its geometric centre).

Question

Moment of inertia of a square plate of mass 'm' and side 'a' about the given axis is equal to (axis is in the plane of the plate and passing through its geometric centre). <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-tiqvrhtwuc9ctyi0.jpg" /> (A) (m a2/6) (B) (m a2/12) (C) (m a2/24) (D) (m a2/48)

Tardigrade Admin · Accepted Answer

Using perpendicular axis theorem Iz=I+I ⇒ 2I=(m a2/6) ⇒ I=(m a2/12)

Q. Moment of inertia of a square plate of mass $^{'} m^{'}$ and side $^{'} a^{'}$ about the given axis is equal to (axis is in the plane of the plate and passing through its geometric centre).

$\frac{m a ^{2}}{6}$

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

$\frac{m a ^{2}}{24}$

$\frac{m a ^{2}}{48}$

Using perpendicular axis theorem
$I_{z} = I + I$
$\Rightarrow 2 I = \frac{m a ^{2}}{6}$
$\Rightarrow I = \frac{m a ^{2}}{12}$

Q. Moment of inertia of a square plate of mass ′m′ and side ′a′ about the given axis is equal to (axis is in the plane of the plate and passing through its geometric centre).

6ma2​

12ma2​

24ma2​

48ma2​