Class 11PhysicsSystem of Particles and Rotational MotionMix Example - System of Particles and Rotational Motion
MediumState whether the following statements are true or false:
$(1)$ In the law of conservation of momentum, the center of mass velocity remains constant.
$(2)$ "If the resultant of internal forces on a system is zero, then the total linear momentum of the system remains constant." This is the statement of the law of conservation of linear momentum.
$(3)$ The position of the center of mass of a rigid body must always be inside the rigid body.
$(4)$ All particles of a rigid body undergoing rotational motion have the same linear velocity.
$(1)$ In the law of conservation of momentum, the center of mass velocity remains constant.
$(2)$ "If the resultant of internal forces on a system is zero, then the total linear momentum of the system remains constant." This is the statement of the law of conservation of linear momentum.
$(3)$ The position of the center of mass of a rigid body must always be inside the rigid body.
$(4)$ All particles of a rigid body undergoing rotational motion have the same linear velocity.
(D) $(1)$ False. The velocity of the center of mass remains constant if the net external force is zero.
$(2)$ False. The statement should refer to the resultant of external forces, not internal forces.
$(3)$ False. The center of mass can be located outside the body (e.g., a ring).
$(4)$ False. In rotational motion, all particles have the same angular velocity, but their linear velocities depend on their distance from the axis of rotation $(v = r\omega)$.
$(2)$ False. The statement should refer to the resultant of external forces, not internal forces.
$(3)$ False. The center of mass can be located outside the body (e.g., a ring).
$(4)$ False. In rotational motion, all particles have the same angular velocity, but their linear velocities depend on their distance from the axis of rotation $(v = r\omega)$.
Explore More
Similar Questions
Fill in the blanks:
$(1)$ If $|\vec{A} \times \vec{B}| = \vec{A} \cdot \vec{B}$,then the angle between $\vec{A}$ and $\vec{B}$ is ............ .
$(2)$ The angle between the angular momentum and linear momentum of a particle in rotational motion is ............ .
$(3)$ $A$ force $F\hat{k}$ acts on a particle having position vector $(2\hat{i} + \hat{j})$. The torque acting on the particle is ............ .
$(1)$ If $|\vec{A} \times \vec{B}| = \vec{A} \cdot \vec{B}$,then the angle between $\vec{A}$ and $\vec{B}$ is ............ .
$(2)$ The angle between the angular momentum and linear momentum of a particle in rotational motion is ............ .
$(3)$ $A$ force $F\hat{k}$ acts on a particle having position vector $(2\hat{i} + \hat{j})$. The torque acting on the particle is ............ .
Medium
View SolutionThree particles each of mass $m$ are located at the vertices of an equilateral triangle $ABC$. They start moving with equal speeds $v$ each along the medians of the triangle and collide at its centroid $G$. If after collision,$A$ comes to rest and $B$ retraces its path along $GB$,then $C$
Difficult
View Solution$A$ solid sphere of mass $M$ and radius $R$ has a moment of inertia $I$ about its diameter. It is recast into a disc of thickness $t$ whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains $I$. The radius of the disc will be:
In the figure shown,the plank is being pulled to the right with a constant speed $v$. If the cylinder does not slip,then:
Difficult
View Solution$A$ uniform rod of length $2L$ has one end on a horizontal floor. It is inclined at an angle $\alpha$ to the horizontal floor. It falls without slipping,rotating about the point of contact. Its angular velocity when it hits the horizontal floor will be:
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo