(C) The moment of inertia of a sphere about an axis passing through its centre is $I_{cm} = \frac{2}{5}MR^2$.Using the parallel axis theorem,the momen

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

(C) The moment of inertia of a sphere about an axis passing through its centre is $I_{cm} = \frac{2}{5}MR^2$.Using the parallel axis theorem,the moment of inertia $I$ about a tangent axis is $I = I_{cm} + MR^2$.Substituting the values,$I = \frac{2}{5}MR^2 + MR^2 = \frac{7}{5}MR^2$.The radius of gyration $K$ is defined by $I = MK^2$.Therefore,$MK^2 = \frac{7}{5}MR^2$.Solving for $K$,we get $K = \sqrt{\frac{7}{5}}R$.

Class 11 Physics System of Particles and Rotational Motion Moment of Inertia and Radius of gyration

Medium

The moment of inertia of a sphere of mass $M$ and radius $R$ about an axis passing through its centre is $\frac{2}{5} M R^2$. The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

A
$ \frac{7}{5}R $
B
$ \frac{3}{5}R $
C
$ \sqrt{\frac{7}{5}} R $
D
$ \sqrt{\frac{3}{5}} R $

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Moment of Inertia and Radius of gyration

Moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is

MediumAIEEE 2002

View Solution

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

MediumAP EAMCET 2025

View Solution

$A$ rod has a length of $1 \ m$ and a mass of $0.12 \ kg$. The moment of inertia about an axis passing through its center and perpendicular to its length is ...... $kg \cdot m^2$.

Easy

View Solution

$A$ circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$,and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{t}{4}$. The ratio of the moment of inertia $\frac{I_Y}{I_X}$ is:

Medium

View Solution

Two discs of the same material and thickness have radii $0.2\, m$ and $0.6\, m.$ Their moments of inertia about their axes will be in the ratio

Medium

View Solution

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

The moment of inertia of a sphere of mass $M$ and radius $R$ about an axis passing through its centre is $\frac{2}{5} M R^2$. The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

Similar Questions

Moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

$A$ rod has a length of $1 \ m$ and a mass of $0.12 \ kg$. The moment of inertia about an axis passing through its center and perpendicular to its length is ...... $kg \cdot m^2$.

$A$ circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$,and another disc $Y$ of radius $4R$ is made from an iron plate of thickness $\frac{t}{4}$. The ratio of the moment of inertia $\frac{I_Y}{I_X}$ is:

Two discs of the same material and thickness have radii $0.2\, m$ and $0.6\, m.$ Their moments of inertia about their axes will be in the ratio

Vedclass Test Series

Exam Paper Generator

Online Exam Module