A thin circular disc is in the xy plane as sh | vedclass

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

Question

(C) The moment of inertia of a circular disc of mass $m$ and radius $R$ about an axis passing through its center of mass $(C.M.)$ and perpendicular to

Vedclass · Accepted Answer

$1:3$

Vedclass · Answer

(C) The moment of inertia of a circular disc of mass $m$ and radius $R$ about an axis passing through its center of mass $(C.M.)$ and perpendicular to its plane is given by:$I_z = \frac{1}{2} mR^2$The axis $z'$ is a tangential axis parallel to the $z$-axis. According to the parallel axis theorem,the moment of inertia about an axis parallel to the central axis is given by $I = I_{cm} + md^2$,where $d$ is the distance between the axes. Here,$d = R$.$I_{z'} = I_z + mR^2 = \frac{1}{2} mR^2 + mR^2 = \frac{3}{2} mR^2$The ratio of the moment of inertia about $z$ and $z'$ axes is:$\frac{I_z}{I_{z'}} = \frac{\frac{1}{2} mR^2}{\frac{3}{2} mR^2} = \frac{1}{3}$Thus,the ratio is $1:3$.

$A$ thin circular disc is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z'$ axes will be

Similar Questions

The moment of inertia of a uniform circular disc of radius $R$ and mass $M$ about an axis touching the disc at its diameter and normal to the disc is

From a uniform circular disc of radius $R$ and mass $9M$,a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through the centre of the original disc is

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 $BB'$.

$A$ solid cylinder of length $L = 80 \, \text{cm}$ and mass $M$ has a radius $r = 20 \, \text{cm}$. Calculate the density of the material used if the moment of inertia of the cylinder about an axis $CD$ parallel to the central axis $AB$ (as shown in the figure) is $2.7 \, \text{kg m}^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module