(D) The radius of gyration $K$ of a body is defined as $K = \sqrt{\frac{\sum m_i r_i^2}{M}}$,where $M$ is the total mass and $r_i$ is the distance of

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

If both the $Assertion$ and $Reason$ are incorrect.

(D) The radius of gyration $K$ of a body is defined as $K = \sqrt{\frac{\sum m_i r_i^2}{M}}$,where $M$ is the total mass and $r_i$ is the distance of the $i$-th particle from the axis of rotation.It is not a constant quantity because its value depends on the position and orientation of the axis of rotation.Therefore,the $Assertion$ is incorrect.The $Reason$ correctly defines the radius of gyration as the root mean square distance of the particles from the axis of rotation.Thus,the $Assertion$ is incorrect,but the $Reason$ is correct.

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

Easy

$Assertion$ : Radius of gyration of a body is a constant quantity.
$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.

AIIMS 2017 All AIIMS

A
If both $Assertion$ and $Reason$ are correct and the $Reason$ is a correct explanation of the $Assertion$.
B
If both $Assertion$ and $Reason$ are correct but $Reason$ is not a correct explanation of the $Assertion$.
C
If the $Assertion$ is correct but $Reason$ is incorrect.
D
If both the $Assertion$ and $Reason$ are incorrect.

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

Previous Year

AIIMS 2017 Paper All AIIMS years →

The moments of inertia of a non-uniform circular disc (of mass $M$ and radius $R$) about four mutually perpendicular tangents $AB, BC, CD, DA$ are $I_1, I_2, I_3$ and $I_4$,respectively (the square $ABCD$ circumscribes the circle). The distance of the centre of mass of the disc from its geometrical centre is given by

KVPY 2015

View Solution

$A$ light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

MediumNEET 2016

View Solution

$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

EasyAIPMT 2008

View Solution

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

MediumMHT CET 2016

View Solution

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

Difficult

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

$Assertion$ : Radius of gyration of a body is a constant quantity.$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.

Similar Questions

$A$ light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$Assertion$ : Radius of gyration of a body is a constant quantity.
$Reason$ : The radius of gyration of a body about an axis of rotation may be defined as the root mean square distance of the particles from the axis of rotation.