The moment of inertia of a rod of length l ab | vedclass

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

Question

(C) The moment of inertia of a rod of length $l$ and mass $m$ about an axis passing through its centre and perpendicular to its length is $I = \frac{m

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) The moment of inertia of a rod of length $l$ and mass $m$ about an axis passing through its centre and perpendicular to its length is $I = \frac{ml^2}{12}$.Thus,$ml^2 = 12I$.For a regular hexagon,the distance $x$ from the centre $O$ to the centre of each rod is the apothem of the hexagon. Since the hexagon is made of six equilateral triangles with side length $l$,the distance $x = l \sin(60^\circ) = \frac{\sqrt{3}}{2}l$.Using the parallel axis theorem,the moment of inertia of one rod about the axis passing through $O$ and perpendicular to the plane is $I_{	ext{rod}} = I_{	ext{cm}} + mx^2 = \frac{ml^2}{12} + m\left(\frac{\sqrt{3}}{2}light)^2 = \frac{ml^2}{12} + \frac{3ml^2}{4} = \frac{ml^2 + 9ml^2}{12} = \frac{10ml^2}{12} = \frac{5ml^2}{6}$.The total moment of inertia of the system of six rods is $I_{	ext{system}} = 6 	imes I_{	ext{rod}} = 6 	imes \frac{5ml^2}{6} = 5ml^2$.Substituting $ml^2 = 12I$,we get $I_{	ext{system}} = 5(12I) = 60I$.

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of a hexagonal shape formed by six such rods,about an axis passing through its centre of mass and perpendicular to its plane,will be (in $I$)

Similar Questions

The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between the center and the end is:

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

For which of the following objects can the moment of inertia $NOT$ be found using the perpendicular axis theorem?

Will the theorem of perpendicular axis be applicable to a solid sphere?

For the given uniform square lamina $ABCD$,whose centre is $O$,which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module