System of Parti...

In which of the following cases the centre of mass of a rod is certainly not at its geometrical centre?

Water is drawn from a well in a $$5\ kg$$ drum of capacity $$55\ L$$ by two ropes connected to the top of the drum. The linear mass density of each rope is $$0.5\ kgm^{-1}$$. The work done in lifting water to the ground from the surface of water in the well $$20\ m$$ below is $$[g=10\ ms^{-2}]$$

A lady dancer is dancing on a turn table. During dancing, she stretches her hands. Then:

Mark the correct option or options 

Consider the following two statements :
(A) Linear momentum of the system remains constant.
(B) Centre of mass of the system remains at rest.

The graph between kinetic energy and momentum of a particle is plotted as shown in Fig. The mass of the moving particle is?

A cracker is thrown into air with a velocity of $$10$$ m/s at an angle of $$45^o$$ with the vertical. When it is at a height of $$0.5$$m from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of $$1$$m from the ground? ($$g=10m/s^2$$)

A ball falls vertically onto a floor with momentum p, and then bounces repeatedly. If the coefficient of restitution is e, then the total momentum impareted by the ball on the floor till the ball comes to rest is?

A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass.

A train of mass M is moving on a circular track of radius 'R' with constant speed V. The length of the train is half of the perimeter of the track. The linear momentum of the train will be?