Consider a uniform square plate of side 'a' a | vedclass

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

Question

(A) The moment of inertia of a square plate of side '$a$' and mass '$m$' about an axis passing through its center of mass and perpendicular to its pla

Vedclass · Accepted Answer

$\frac{2}{3}ma^2$

Vedclass · Answer

(A) The moment of inertia of a square plate of side '$a$' and mass '$m$' about an axis passing through its center of mass and perpendicular to its plane is given by:$I_{cm} = \frac{1}{12}m(a^2 + a^2) = \frac{ma^2}{6}$According to the parallel axis theorem,the moment of inertia about an axis passing through a corner and perpendicular to the plane is:$I = I_{cm} + md^2$Here,'$d$' is the distance from the center of the square to the corner. For a square of side '$a$',the diagonal is '$a\sqrt{2}$',so the distance from the center to a corner is:$d = \frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$Substituting the values:$I = \frac{ma^2}{6} + m\left(\frac{a}{\sqrt{2}}\right)^2$$I = \frac{ma^2}{6} + \frac{ma^2}{2}$$I = \frac{ma^2 + 3ma^2}{6} = \frac{4ma^2}{6} = \frac{2}{3}ma^2$

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Similar Questions

Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

From a circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $O$ is:

Four identical solid spheres each of mass $m$ and radius $a$ are placed with their centres on the four corners of a square of side $b$. The moment of inertia of the system about one side of the square is:

$A$ disc and a ring both have the same mass and radius. The ratio of the moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

Four holes of radius $R$ are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about the $z-$ axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module