(C) In the absence of any external torque,the angular momentum of the system remains conserved.$L_{initial} = L_{final}$$I \omega = I' \omega'$Initial

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

(C) In the absence of any external torque,the angular momentum of the system remains conserved.$L_{initial} = L_{final}$$I \omega = I' \omega'$Initially,the moment of inertia of the ring about its axis is $I = MR^2$.When two objects of mass $m$ are placed at opposite ends of a diameter,they are at a distance $R$ from the axis of rotation. The new moment of inertia becomes $I' = MR^2 + mR^2 + mR^2 = (M + 2m)R^2$.Using the conservation of angular momentum:$MR^2 \omega = (M + 2m)R^2 \omega'$$\omega' = \frac{MR^2 \omega}{(M + 2m)R^2}$$\omega' = \frac{\omega M}{M + 2m}$

Class 11 Physics System of Particles and Rotational Motion Conservation of angular momentum (combined translation and rotational motion)

Difficult

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are gently placed at opposite ends of a diameter of the ring. The new angular velocity of the ring will be

A
$\frac{\omega M}{M + m}$
B
$\frac{\omega (M - 2m)}{M + 2m}$
C
$\frac{\omega M}{M + 2m}$
D
$\frac{\omega (M + 2m)}{M}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Conservation of angular momentum (combined translation and rotational motion)

Assertion $:-$ When no external torque is applied and moment of inertia of a rotating body changes,then its angular momentum remains conserved,but its kinetic energy changes.
Reason $:-$ Angular momentum does not depend upon moment of inertia of the body.

Medium

View Solution

$A$ disc of mass $1 \, kg$ and radius $0.1 \, m$ is rotating with angular velocity $20 \, rad/s$. What is the angular velocity (in $rad/s$) if a mass of $0.5 \, kg$ is placed on the circumference of the disc?

Difficult

View Solution

$A$ body changes its angular speed from $\omega_1$ to $\omega_2$ without any external torque applied. This change is due to a change in its moment of inertia. What is the ratio of the radii of gyration in the two cases?

Easy

View Solution

$A$ person of $80\, kg$ mass is standing on the rim of a circular platform of mass $200\, kg$ rotating about its axis at $5$ revolutions per minute $(rpm)$. The person now starts moving towards the centre of the platform. What will be the rotational speed (in $rpm$) of the platform when the person reaches its centre?

MediumJEE MAIN 2020

View Solution

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,the duration of the new day will be nearly:

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

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are gently placed at opposite ends of a diameter of the ring. The new angular velocity of the ring will be

Similar Questions

Assertion $:-$ When no external torque is applied and moment of inertia of a rotating body changes,then its angular momentum remains conserved,but its kinetic energy changes.Reason $:-$ Angular momentum does not depend upon moment of inertia of the body.

$A$ disc of mass $1 \, kg$ and radius $0.1 \, m$ is rotating with angular velocity $20 \, rad/s$. What is the angular velocity (in $rad/s$) if a mass of $0.5 \, kg$ is placed on the circumference of the disc?

$A$ body changes its angular speed from $\omega_1$ to $\omega_2$ without any external torque applied. This change is due to a change in its moment of inertia. What is the ratio of the radii of gyration in the two cases?

If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass,the duration of the new day will be nearly:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion $:-$ When no external torque is applied and moment of inertia of a rotating body changes,then its angular momentum remains conserved,but its kinetic energy changes.
Reason $:-$ Angular momentum does not depend upon moment of inertia of the body.