The moment of inertia of a thin square plate | vedclass

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

Question

(D) According to the theorem of perpendicular axes,the moment of inertia $I_z$ of a planar body about an axis perpendicular to its plane and passing t

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

(D) According to the theorem of perpendicular axes,the moment of inertia $I_z$ of a planar body about an axis perpendicular to its plane and passing through a point $O$ is equal to the sum of the moments of inertia about two mutually perpendicular axes in the plane of the body,both passing through $O$.In the given figure,axes $1$ and $2$ are the diagonals of the square,which are mutually perpendicular. Thus,$I_0 = I_1 + I_2$.Axes $3$ and $4$ are lines passing through the centre $O$ and parallel to the sides of the square. These are also mutually perpendicular. Thus,$I_0 = I_3 + I_4$.Furthermore,due to the symmetry of the square,the moment of inertia about any axis passing through the centre and lying in the plane of the plate is the same if the angle of the axis is the same relative to the sides. Specifically,for a square plate,$I_1 = I_2 = I_3 = I_4 = \frac{ML^2}{12}$.Therefore,$I_0 = I_1 + I_2 = I_3 + I_4 = I_1 + I_3$ (since $I_1 = I_3$).Thus,all the given options are correct.

Similar Questions

Four thin metal rods,each of mass $M$ and length $L$,are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

The string of a simple pendulum is replaced by a uniform rod of length $L$ and mass $M$. If the mass of the bob of the pendulum is $m$,then for small oscillations its time period would be (assume radius of bob $r << L$):

The moment of inertia of a uniform hollow hemisphere about the given axes $I_A$ and $I_B$ is:

$A$ thin metal wire of length $L$ and uniform linear mass density $Q$ is bent into a circular coil with $O$ as the center. The moment of inertia of the coil about the axis $XX'$ is:

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its midpoint and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

Vedclass Test Series

Exam Paper Generator

Online Exam Module