The nucleus Fe²⁷ emits a \(\gamma \)-ray of energy 14.4 keV. If the mass of the nucleus is 56.935 amu, calculate the recoil energy of the nucleus.

One day Pawan went to super market to purchase some groceries. There he saw an old lady struggling with her shopping. He immediately showed her the lift and explained to her how she can carry her goods from one floor to the other. Even then the old lady showed hesitation to use the lift. On seeing this, Pawan took the lady into the lift and showed her how to operate the lift. The old lady was very happy and easily finished her shopping.
(i) An elevator which can carry a maximum load of 1800 of 2m/s. The frictional force opposing he motion is 4000 N.Determine the maximum power delivered by the motor to the elevator in horse power.

Rocket Propulsion
A toy rocket of mass 0.1 kg has a small fuel of mass 0.02 kg which it burns out in 3 s. Starting from rest on horizontal smooth track it gets a speed of 20 ms^-1 after the fuel is burnt out. What is the approximate thrust of the rocket ? What is the energy content per unit mass of the fuel ? (Ignore the small mass variation of the rocket of the rocket during fuel burning).

When a pebble Hits the Ground
Consider a drop of small pebble of mass 1.00 g falling from a cliff of height 1.00 km. It hits the ground with a speed of 50.0 ms^-1. What is the work done by the unknown resistive force ?

A railway carriage of mass 9000kg moving with a speed of 36km/h collides with stationary carriage of the same mass. After the collision, the carriage get coupled of the same mass. After the collision, the carriage get coupled and move together. What is their common speed after collision? what type of collision is this?

The sign of work done by a force on a body is important to understand .State carefully if the following quantities are positive or negative
(i) Work done by gravitational force in the above cases.
(ii) Work done by friction on a body sliding down on  inclined plane.
(iii) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity
(iv) Work done by the resistive force  of air on a vibrating pendulum in bringing it to rest .

A particle of mass moving with an initial velocity u collides inelastically with a particle of mass M initially at rest. if the collision is completely inelastic, then find expressions for 
final velocity of combined entity and

A 1 kg block situated on a rough incline is connected to a spring with spring constant 100 Nm^-1 as shown in Figure. The block is released from rest with the spring in the unstretched position. The block moves 10 cm down the incline before coming to rest. Find the coefficient offriction between the block and the incline. Assume that the spring has negligible mass and the pulley is frictionless.