(D) The velocity of the center of mass $(v_{cm})$ is related to the total external force $(F_{ext})$ by the equation $F_{ext} = M a_{cm} = M (dv_{cm}/

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

Statement-$1$ is False,Statement-$2$ is True.

(D) The velocity of the center of mass $(v_{cm})$ is related to the total external force $(F_{ext})$ by the equation $F_{ext} = M a_{cm} = M (dv_{cm}/dt)$.If the total external force is zero,then $a_{cm} = 0$,which implies $v_{cm}$ is constant.$STATEMENT-1$ states that there is no external torque. The absence of external torque implies that the angular momentum is conserved,but it does not necessarily imply that the total external force is zero.For example,a couple acting on a body produces torque but zero net force. Thus,$v_{cm}$ may change if there is a net force,even if there is no net torque.Therefore,$STATEMENT-1$ is False.$STATEMENT-2$ is a fundamental principle of mechanics (Law of Conservation of Linear Momentum) and is True.Thus,$STATEMENT-1$ is False and $STATEMENT-2$ is True.

Class 11 Physics System of Particles and Rotational Motion Mix Example - System of Particles and Rotational Motion

Difficult

$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because
$STATEMENT-2$ The linear momentum of an isolated system remains constant.

IIT 2007 All IIT

AIIMS 2015 All AIIMS

A
Statement-$1$ is True,Statement-$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$.
B
Statement-$1$ is True,Statement-$2$ is True; Statement-$2$ is $NOT$ a correct explanation for Statement-$1$.
C
Statement-$1$ is True,Statement-$2$ is False.
D
Statement-$1$ is False,Statement-$2$ is True.

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Mix Example - System of Particles and Rotational Motion

Previous Year

IIT 2007 Paper All IIT years →

Previous Year

AIIMS 2015 Paper All AIIMS years →

The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is $I$. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it so that their centres coincide. If both rings are rotating about the same axis, then the loss in kinetic energy is

DifficultMHT CET 2026

View Solution

$A$ uniform cylinder of radius $R$ is spun with angular velocity $\omega$ about its axis and then placed into a corner. The coefficient of friction between the cylinder and the planes is $\mu$. The number of turns taken by the cylinder before stopping is given by

View Solution

$A$ metal rod of length $L$ and mass $m$ is pivoted at one end. $A$ thin disk of mass $M$ and radius $R$ $(R < L)$ is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case $A$) The disc is not free to rotate about its center and (case $B$) the disc is free to rotate about its center. The rod-disc system performs $SHM$ in a vertical plane after being released from the same displaced position. Which of the following statement$(s)$ is (are) true?

IIT 2011

View Solution

Two cylindrical hollow drums of radii $R$ and $2R$ and of a common height $h$ are rotating with angular velocities $\omega$ (anti-clockwise) and $\omega$ (clockwise) respectively. Their axes,which are fixed,are parallel and in a horizontal plane separated by $3R$. They are now brought into contact.
$(a)$ Show the frictional forces just after contact.
$(b)$ Identify forces and torques external to the system just after contact.
$(c)$ What would be the ratio of final angular velocities when friction ceases?

Difficult

View Solution

$A$ ring,a solid sphere,and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest?

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

$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because$STATEMENT-2$ The linear momentum of an isolated system remains constant.

Similar Questions

$A$ uniform cylinder of radius $R$ is spun with angular velocity $\omega$ about its axis and then placed into a corner. The coefficient of friction between the cylinder and the planes is $\mu$. The number of turns taken by the cylinder before stopping is given by

$A$ ring,a solid sphere,and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because
$STATEMENT-2$ The linear momentum of an isolated system remains constant.