Centre of Mass, Linear Momentum, Collision Physics - Centre of Mass, Linear Momentum, Collision

Internal forces can change:

1. The linear momentum but not the kinetic energy.
2. The kinetic energy but not the linear momentum.
3. Linear momentum as well as kinetic energy.
4. Neither the linear momentum nor the kinetic energy.

In an inelastic collision:

1. The initial kinetic energy is equal to the final kinetic energy.
2. The final kinetic energy is less than the initial kinetic energy.
3. The kinetic energy remains constant.
4. The kinetic energy first increases then decreases.

The quantities remaining constant in a collisions are

1. Momentum, kinetic energy and temperature.
2. Momentum and kinetic energy but not temperature.
3. Momentum and temperature but not kinetic energy.
4. Momentum, but neither kinetic energy nor temperature.

If the external force acting on a system have zero resultant, the centre of mass:

1. Must not move.
2. Must not accelerate.
3. May move.
4. May accelerate.

A ball is moved on a horizontal table with some velocity. The ball stops after moving some distance. Which external force is responsible for the change in the momentum of the ball?

If all the particle of a system lie in a cube, is it neccesary that the centre of mass be in the cube?

Suppose we define a quantity 'Linear Pomentum' as linear pomentum = mass × speed. The linear pomentum of a system of particles is the sum of linear pomenta of the individual particles. Can we state a principle of conservation of linear pomentum as ''linear pomentum of a system remains constant if no external force acts on it?''

If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?

Use the definition of linear pomentum from the previous question. Can we state the principle of conservation of linear pomentum for a single particle?

To accelerate a car we ignite petrol in the engine of the car. Since only an external force can accelerate the centre of mass, is it proper to say that ''the force generated by the engine accelerates the car?''

Which of the two persons shown in figure is more likely to fall down? Which external force is responsible for his falling down?

A railroad car of mass M is at rest on frictionless rails when a man of mass m starts moving on the car towards the engine. If the car recoils with a speed v backward on the rails, with what velocity is the man approaching the engine?

If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily non-zero?

Can the centre of mass of a body be at a point outside the body?

A 60kg man skating with a speed of 10m/s collides with a 40kg skater at rest and they cling to each other. Find the loss of kinetic energy during the collision.

A ball falls on the ground from a height of 2.0m and rebounds up to a height of 1.5m. Find the coefficient of restitution.

Two blocks of mares 10kg and 20kg are placed on the X-axis. The first mass is moved on the axis by a distance of 2cm. By what distance should the second mass be moved to keep the position of the centre of mass unchanged?

Figure shows a small block of mass m which is started with a speed v on the horizontal part of the bigger block of mass M placed on a horizontal floor. The curved part of the surface shown is semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

The weight Mg of an extended body is generally shown in a diagram to act through the centre of mass. Does it mean that the earth does not attract other particles?

Consider a gravity-free hall in which an experimenter of mass 50kg is resting on a 5kg pillow, 8ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process.

A fat person is standing on a light plank floating on a calm lake. The person walks from one end to the other on the plank. His friend sitting on the shore watches him and finds that the person hardly moves any distance because the plank moves backward about the same distance as the person moves on the plank. Explain.

A collision experiment is done on a horizontal table kept in an elevator. Do you expect a change in the results if the elevator is accelerated up or down because of the noninertial character of the frame?

Two friends A and B (each weighing 40kg) are sitting on a frictionless platform some distance d apart. A rolls a ball of mass 4kg on the platform towards B which B catches. Then B rolls the ball towards A and A catches it. The ball keeps on moving back and forth between A and B. The ball has a fixed speed of 5m/s on the platform.

1. Find the speed of A after he rolls the ball for the first time.
2. Find the speed of A after he catches the ball for the first time.
3. Find the speeds of A and B after the ball has made 5 round trips and is held by A.
4. How many times can A roll the ball?
5. Where is the centre of mass of the system ''A + B + ball'' at the end of the n^th trip?

Two masses m₁ and m₂ are connected by a spring of spring constant k and are placed on a frictionless horizontal surface. Initially the spring is stretched through a distance x₀ when the system is released from rest. Find the distance moved by the two masses before they again come to rest.

Figure shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed v and the system is left to itself. Assume that all the surfaces are frictionless.

1. Find the speed of the larger block when the smaller block is sliding on the vertical part.
2. Find the speed of the smaller mass when it breaks off the larger mass at height h.
3. Find the maximum height (from the ground) that the smaller mass ascends.
4. Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.

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Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii R₁ and R₂.

A block of mass 200g is suspended through a vertical spring. The spring is stretched by 1.0cm when the block is in equilibrium. A particle of mass 120g is dropped on the block from a height of 45cm. The particle sticks to the block after the impact. Find the maximum extension of the spring. Take g = 10m/s².