Class 11PhysicsSystem of Particles and Rotational MotionEffect of Internal and External Force on Centre of Mass
EasyState Newton's second law for a system of particles.
(N/A) For a system of particles,Newton's second law states that the total external force acting on the system is equal to the rate of change of the total linear momentum of the system.
Mathematically,it is expressed as: $\vec{F}_{ext} = \frac{d\vec{P}}{dt}$,where $\vec{F}_{ext}$ is the sum of all external forces acting on the system and $\vec{P}$ is the total linear momentum of the system.
Since the total linear momentum $\vec{P}$ is equal to $M\vec{v}_{cm}$ (where $M$ is the total mass and $\vec{v}_{cm}$ is the velocity of the center of mass),the law can also be written as: $\vec{F}_{ext} = M\vec{a}_{cm}$,where $\vec{a}_{cm}$ is the acceleration of the center of mass of the system.
Mathematically,it is expressed as: $\vec{F}_{ext} = \frac{d\vec{P}}{dt}$,where $\vec{F}_{ext}$ is the sum of all external forces acting on the system and $\vec{P}$ is the total linear momentum of the system.
Since the total linear momentum $\vec{P}$ is equal to $M\vec{v}_{cm}$ (where $M$ is the total mass and $\vec{v}_{cm}$ is the velocity of the center of mass),the law can also be written as: $\vec{F}_{ext} = M\vec{a}_{cm}$,where $\vec{a}_{cm}$ is the acceleration of the center of mass of the system.
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Similar Questions
Choose the correct statement$(s)$:
$(A)$ The position of the centre of mass of a system is dependent on the choice of coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.
$(A)$ The position of the centre of mass of a system is dependent on the choice of coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.
$Assertion$ : If no external force acts on a system of particles,then the centre of mass will not move in any direction.
$Reason$ : If net external force is zero,then the linear momentum of the system changes.
$Reason$ : If net external force is zero,then the linear momentum of the system changes.
The multiplication of the total mass of a system and the acceleration of its centre of mass denotes what?
Easy
View SolutionIf a force $10 \hat{i} + 15 \hat{j} + 25 \hat{k}$ acts on a system and gives an acceleration $2 \hat{i} + 3 \hat{j} - 5 \hat{k}$ to the centre of mass of the system,the mass of the system is
Medium
View SolutionTwo spheres of masses $2M$ and $M$ are initially at rest at a distance $R$ apart. Due to mutual force of attraction,they approach each other. When they are at separation $R/2$,the acceleration of the centre of mass of the system would be .......
Easy
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