If the total external forces on the system of particle is zero, then find the velocity and acceleration of its centre of mass.

If the external force acting on a system of particle is zero then …………..

What is the total momentum of the system of particle?

In a SHM at which point velocity and acceleration is zero?

Which types of force acting on the system of particle?

If net force on a system of particles is zero. Then {:(,"Column I",,"Column II",),((A),"Acceleration of centre of mass",(p),"Constant",),((B),"Velocity of centre of mass",(q),"Zero",),((C ),"Momentum of centre of mass",(r ),"May br zero",),((D),"Velocity of an individual particle of the system",(s),"May be constant",):}

The multiplication of total mass of system and the acceleration of its centre of mass denote what?

Show that the total momentum of system of particles is equal to the product of total mass of system and velocity of centre of mass.

If the resultant external force on a system is zero, then the total…………of system remains constant.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass : (a) Show p=p_(i).+m_(i)V where p_(i) is the momentum of the ith particle (of mass m_(i) ) and p_(i).=m_(i)v_(i). . Note v_(i). is the velocity of the i^(th) particle relative to the centre of mass Also, prove using the definition of the centre of mass Sigmap_(i).=0 (b) Show K=K.+(1)/(2)MV^(2) where K is the total kinetic energy of the system of particles, K. is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and (1)/(2)MV^(2) is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14). (c ) Show vecL=vecL.+vecRxxvec(MV) where vecL.=Sigmavec(r_(i)).xxvec(p_(i)). is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vec(r._(i))=vec(r_(i))-vecR , rest of the notation is the velcities taken relative to the centre of mass. Remember vec(r._(i))=vec(r_(i))-vecR rest of the notation is the standard notation used in the chapter. Note vecL , and vec(MR)xxvecV can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles. (d) Show vec(dL.)/(dt)=sumvec(r_(i).)xxvec(dp.)/(dt) Further, show that vec(dL.)/(dt)=tau._(ext) where tau._(ext) is the sum of all external torques acting on the system about the centre of mass. (Hint : Use the definition of centre of mass and Newton.s Thrid Law. Assume the internal forces between any two particles act along the line joining the particles.)

Write the expression of centre of mass of a system of .n. particles and derive the formula of force acting on its centre of mass.