Motion of Centre of Mass

A bullet of mass m moving at a speed v hits a ball of mass M kept at rest. A small part having mass m breaks from the ball and sticks to the bullet. The remaining ball is found to move at a speed v₁ in the direction of the bullet. Find the velocity of the bullet after the collision. 

Read each statement below carefully, and state, with reasons, if it is true or false;

The instantaneous acceleration of the point of contact during rolling is zero.

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 in semicircular. All the surfaces are frictionless. Find the speed of the bigger block when the smaller block reaches the point A of the surface. 

Read each statement below carefully, and state, with reasons, if it is true or false;

 During rolling, the force of friction acts in the same direction as the direction of motion of the CM of the body

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

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"?

Three identical spheres, each of mass M, are placed at the comers of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

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.