Obtain Newton's second law for a system of particles and write its statement.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The total linear momentum of a system of particles is given by $\vec{p} = M\vec{v}_{cm}$,where $M$ is the total mass of the system and $\vec{v}_{cm}$ is the velocity of the centre of mass.
Taking the derivative with respect to time $t$ on both sides:
$\frac{d\vec{p}}{dt} = M \frac{d\vec{v}_{cm}}{dt}$
Since the acceleration of the centre of mass is $\vec{a}_{cm} = \frac{d\vec{v}_{cm}}{dt}$,we have:
$\frac{d\vec{p}}{dt} = M\vec{a}_{cm}$
According to the motion of the centre of mass,the net external force acting on the system is $\vec{F}_{ext} = M\vec{a}_{cm}$.
Therefore,substituting this into the equation,we get:
$\frac{d\vec{p}}{dt} = \vec{F}_{ext}$
This is Newton's second law for a system of particles.
Statement: The external force acting on a system of particles is equal to the rate of change of the total linear momentum of the system.

Explore More

Similar Questions

Consider a two-particle system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$,by what distance should the second particle be moved,so as to keep the centre of mass at the same position?

Difficult
View Solution

$A$ system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$,then the distance the second particle should be moved,so as to keep the centre of mass at the same position is

In the given figure,if the speed given to block $A$ is $10\,m/s$ and block $B$ is initially at rest,then the speed of the centre of mass after $10\,s$ will be ....... $m/s$.

Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in the air,

Two particles of masses $m_1$ and $m_2$ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass at any time $t$,when they are at a distance $r$ apart,is

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