Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius,about an axis passing through their axes of symmetry?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The moment of inertia $I$ of a body is given by $I = \sum m_i r_i^2$,where $m_i$ is the mass element and $r_i$ is its perpendicular distance from the axis of rotation.
For a hollow cylinder of mass $M$ and radius $R$,all its mass is distributed at a distance $R$ from the axis of symmetry. Thus,its moment of inertia is $I_{cylinder} = MR^2$.
For a solid sphere of mass $M$ and radius $R$,the mass is distributed throughout its volume,meaning most of its mass lies at a distance $r < R$ from the axis of symmetry. Its moment of inertia is $I_{sphere} = \frac{2}{5}MR^2$.
Since $\frac{2}{5}MR^2 < MR^2$,the solid sphere has a smaller moment of inertia than the hollow cylinder.

Explore More

Similar Questions

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

$A$ circular disc is to be made by using iron and aluminium,so that it acquires a large moment of inertia about its geometrical axis. This is possible with:

Two rods of equal length $(l)$ and equal mass $M$ are kept along the $x$ and $y$ axes respectively,such that their center of mass lies at the origin. The moment of inertia about the line $y = x$ is ...........

Difficult
View Solution

Two spheres $A$ and $B$,each of mass $5 \ kg$,are attached to the ends of a light rod of length $1 \ m$. Treating the spheres as point masses,find the ratio of the moment of inertia of the system about an axis passing through $A$ to that about an axis passing through the center of the rod,both axes being perpendicular to the rod.

The radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo