A circular disc D_1 of mass M and radius R ha | vedclass

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

Question

(B) The total moment of inertia $I$ of the system is the sum of the moments of inertia of the three discs about the axis $OO'$.For disc $D_1$,the axis

Vedclass · Accepted Answer

$3MR^2$

Vedclass · Answer

(B) The total moment of inertia $I$ of the system is the sum of the moments of inertia of the three discs about the axis $OO'$.For disc $D_1$,the axis $OO'$ passes through its centre and is perpendicular to its plane. Thus,$I_1 = \frac{1}{2}MR^2$.For discs $D_2$ and $D_3$,the axis $OO'$ is parallel to their diameters and passes at a distance $R$ from their centres. Using the parallel axis theorem,$I_{2,3} = I_{cm} + Md^2 = \frac{1}{4}MR^2 + MR^2 = \frac{5}{4}MR^2$.Since there are two such discs,the total moment of inertia is $I = I_1 + 2 	imes I_{2,3} = \frac{1}{2}MR^2 + 2 	imes (\frac{5}{4}MR^2) = \frac{1}{2}MR^2 + \frac{5}{2}MR^2 = 3MR^2$.

Similar Questions

From a disc of radius $R$,a concentric circular portion of radius $r$ is cut out so as to leave an annular disc of mass $M$. The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is

The moment of inertia of a thin uniform rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

The moment of inertia of a uniform horizontal solid cylinder of mass $M$ about an axis passing through its edge and perpendicular to the axis of the cylinder, when its length is $6$ times its radius $R$, 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 triangular plate $ABC$ of mass $M$ and side $BC = a,$ about an axis passing through $A$ and perpendicular to the plane of the plate is :-

Vedclass Test Series

Exam Paper Generator

Online Exam Module