Question

Obtain Newton's second law for system of particle and write it.​

Answer 1

refer to attachment:-

Answer 2

(Consider ' as vector notation)

(Consider n as subscript)

Linear momentum of a particle is

p'=mv'

Newton's second law written for a single particle is

F'=dp'/dt

For system of n particles, linear momentum of the system is the vector sum of all the individual particles of the system

P'= p1'+p2'+...+pn'

= m1v1+m2v2+...+mnvn

(Where n is a subscript denoting number of particles)

Also MV=m1v1' + m2v2' +...+mnvn'

Therefore P=MV' ---(1)

(Please consider the ' as vector notation)

Differentiating eq (1) wrt time

dP'/dt = MdV'/dt = MA'

Also dP'/dt = Fext

Therefore Fext = MA'

Or

dP'/dt = Fext

This is the statement of newton's third law extended to a system of particles.