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 railway carriage of mass 9,000 kg moving with a speed of 36 km h^-1 strikes a stationary carriage of same mass. After the collision, the carriages get coupled and move together. what is their common speed after collision? Is the collision elastic?

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 ?

A rocket of initial mass 6000 kg ejects mass at a constant rate of 16 kgs^-1 with constant relative speed of 11 kms^-1 . What is the acceleration of the rocket a minute after the blast? (Neglect gravity).

What is the de-Broglie wavelength of a bullet of mass 0.040 kg travelling at the speed of 1.0km/s.

What is the de-Broglie wavelength of a ball of mass 0.060 kg moving at a speed of 1.0 m/s.

A bullet of mass 0.04 kg moving with a speed of 90 ms^-1 enters a heavy wooden block and is stopped after a distance of 60 cm. What is the average resistive force exerted by the block on the bullet?

A girl riding a bicycle along a straight road with a speed of 5 ms^-1 throws a stone of mass 0.5 kg which has a speed of 15 ms^-1 with respect to the ground along her direction of motion. The mass of the girl and bicyle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 50,000 kg is moving with a speed of 36 km h^-1 when the brakes are applied to bring it to rest. In the proces of the system being brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If 90% of energy of te wagon is lost due to friction. calculate the spring constant.

A bullet of mass 25 g moving with a speed of 100 m/s pierces a bag full of sand kept adjacent to a wall. The bullet stops in the bag after 0.05 second. Find The force exerted by the sandbag on the bullet.