When explosion of bomb projected which forces do not contribute in the motion of centre of mass?

Under which force the centre of mass is moving?

Which forces needed for the rotational motion about a fixed axis?

If the explosion in projectile takes place, which force acting its centre of mass?

The masses and radii of the earth an moon are M_(1) and R_(1) and M_(2), R_(2) respectively. Their centres are at a distacne r apart. Find the minimum speed with which the particle of mass m should be projected from a point mid-way between the two centres so as to escape to infinity.

A rod of mass m and length l is hinged at one of its ends A as shown in figure. A force F is applied at a distance x from A . The acceleration of centre of mass varies with x as -

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.)

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

A particle of mass m is projected with speed u at an angle theta with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.

“When a person walk on rough surface then frictional force act in opposite direction of motion” - True or false ?

An object of mass 5 kg is projecte with a velocity of 20ms^(-1) at an angle of 60^(@) to the horizontal. At the highest point of its path , the projectile explodes and breaks up into two fragments of masses 1kg and 4 kg. The fragments separate horizontally after the explosion, which releases internal energy such that K.E. of the system at the highest point is doubled. Calculate the separation betweent the two fragments when they reach the ground.