Moment of inertia of a disc about its own axi | vedclass

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

Question

(A) The moment of inertia $(I)$ of a disc of mass $M$ and radius $R$ about its central axis perpendicular to its plane is given by $I = \frac{1}{2}MR^

Vedclass · Accepted Answer

$\frac{5}{2}I$

Vedclass · Answer

(A) The moment of inertia $(I)$ of a disc of mass $M$ and radius $R$ about its central axis perpendicular to its plane is given by $I = \frac{1}{2}MR^2$.According to the perpendicular axis theorem,the moment of inertia about a diameter $(I_d)$ is $I_d = \frac{I}{2} = \frac{1}{4}MR^2$.To find the moment of inertia about a tangential axis in the plane of the disc,we use the parallel axis theorem: $I_{tangent} = I_d + MR^2$.Substituting $I_d = \frac{I}{2}$ and $MR^2 = 2I$ (since $I = \frac{1}{2}MR^2 \implies MR^2 = 2I$):$I_{tangent} = \frac{I}{2} + 2I = \frac{5}{2}I$.

Moment of inertia of a disc about its own axis is $I$. Its moment of inertia about a tangential axis in its plane is

Similar Questions

Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected at the ends of a massless rod of length $2R$. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

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 circular disc is maximum about an axis perpendicular to the disc and passing through which of the following points?

$A$ rigid body of mass $m$ rotates with angular velocity $\omega$ about an axis at a distance $d$ from its center of mass. The radius of gyration about an axis passing through the center of mass $G$ and parallel to the given axis is $K$. What is the rotational kinetic energy of the body?

Four spheres,each of mass $M$ and diameter $2a$,are placed at the corners of a square of side $b$ as shown in the figure. Calculate the moment of inertia about the axis $BB'$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module