A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of `0.05 kg s^-1`. What is the speed of the trolley after the entire sand bag is empty?

A trolley of mass 200 kg moves with a uniform speed of 36 km/ h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s^-1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with an uniform speed of 7 m s^-1 . It hits the floor of the elevator (length of the elevator = 3 m) and does not- rebound. What is the heat produced by the impact? Would your answer be different if the elevator were stationary?

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m s~1 collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-^1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^-1 in the same direction, with A ahead of B. The driver of B decides to overtake A and accelerates by 1 m//s^-2 . If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

The driver of a three-wheeler moving with a speed of 36 km/ h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 106 kg. What provides the centripetal force required for this purpose - The engine or the rails? What is the angle of banking required to prevent- wearing out of the rail?

A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m - wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it.

A constant force acting on a body of mass 3.0 kg changes its speed from 2.0 m s^-1 to 3.5 m s^-1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force?

Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train,(b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h,just after it is dropped from the window of a train accelerating with 1 ms^2,just after it is dropped from the window of a train accelerating with 1M/S2