Consider a thin uniform square sheet made of | vedclass

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

Question

(D) For a thin uniform square sheet of side $a$ and mass $m$,the moment of inertia about an axis passing through the center and perpendicular to the p

Vedclass · Accepted Answer

$I = \frac{ma^2}{12}$

Vedclass · Answer

(D) For a thin uniform square sheet of side $a$ and mass $m$,the moment of inertia about an axis passing through the center and perpendicular to the plane is $I_z = \frac{ma^2}{6}$.By the perpendicular axis theorem,$I_z = I_x + I_y$,where $I_x$ and $I_y$ are the moments of inertia about the two perpendicular axes passing through the center in the plane of the sheet.Due to symmetry,$I_x = I_y = \frac{ma^2}{12}$.Let $I_d$ be the moment of inertia about a diagonal. By the perpendicular axis theorem applied to the two diagonals (which are also perpendicular to each other and lie in the plane),$I_z = I_{d1} + I_{d2}$.Since the square is symmetric,$I_{d1} = I_{d2} = I$.Thus,$I_z = 2I$,which implies $I = \frac{I_z}{2} = \frac{ma^2/6}{2} = \frac{ma^2}{12}$.Wait,let us re-evaluate: The moment of inertia of a square plate about an axis passing through the center and parallel to a side is $I_{side} = \frac{ma^2}{12}$.The moment of inertia about a diagonal is $I_{diag} = \frac{ma^2}{12}$.Therefore,$I = \frac{ma^2}{12}$.

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and the moment of inertia about one of its diagonals is $I$,then:

Similar Questions

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through a point at a distance $L/4$ from one of its ends and perpendicular to the length of the rod is

The theorem of perpendicular axes is applicable to which type of body?

Three thin metal rods,each of mass $M$ and length $L$,are welded to form an equilateral triangle. The moment of inertia of the composite structure about an axis passing through the centre of mass of the structure and perpendicular to its plane is

$A$ square lamina of side $b$ has the same mass as a disc of radius $R$. The moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

Vedclass Test Series

Exam Paper Generator

Online Exam Module