What is the moment of inertia of a square she | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Side length $= l$. Mass per unit area $= \mu$. Total mass $M = \mu l^2$. For a square sheet,the moment of inertia about an axis passing through it

Vedclass · Accepted Answer

$\frac{\mu l^4}{6}$

Vedclass · Answer

(B) Side length $= l$. Mass per unit area $= \mu$. Total mass $M = \mu l^2$. For a square sheet,the moment of inertia about an axis passing through its centre and parallel to one of its sides is $I_x = I_y = \frac{M l^2}{12}$. By the perpendicular axis theorem,the moment of inertia about an axis passing through the centre and perpendicular to its plane is $I_z = I_x + I_y$. $I_z = \frac{M l^2}{12} + \frac{M l^2}{12} = \frac{2 M l^2}{12} = \frac{M l^2}{6}$. Substituting $M = \mu l^2$,we get $I_z = \frac{(\mu l^2) l^2}{6} = \frac{\mu l^4}{6}$. Thus,the correct option is $B$.

What is the moment of inertia of a square sheet of side $l$ and mass per unit area $\mu$ about an axis passing through the centre and perpendicular to its plane?

Similar Questions

The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

What is the moment of inertia of a ring of mass $M$ and radius $R$ about the axis $PQ$ as shown in the figure?

The moment of inertia of a circular ring of mass $M$ and diameter $r$ about a tangential axis lying in the plane of the ring is

The moment of inertia of a uniform circular ring,having a mass $M$ and a radius $R$,about an axis tangential to the ring and perpendicular to its plane,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module