A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

The work done by the conservative force for a closed path is

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

Two equal masses m₁ and m₂ are moving along the same straight line with velocities 5ms^-1 and -9 ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m₁ and m₂ respectively

A particle free to move along X-axis has potential energy given as U(X)=K(1-e^{\({ -X }^{ 2 }\)} ) ,where k is a positive constant of appropriate dimension. Then ,for -a∞

When a bullet of mass 10g and speed 100ms^-1 penetrates up to distance 1 cm in a human body in rest. The resistance offered by human body is 

The momentum of a body is incresed by 20% . the percentage increases in kinetic energy is 

A body of mass m is accelerated uniformly from rest to a speed v at a time T. The instantaneous power  delivered to the body as a function of times is given 

A train of mass 2\(\times \)10⁵ kg has a constant speed of 20 m/s up a hill inclied at  \(\theta \)  sin^-1(\(\frac { { 1 } }{ { 50 } } \))to the horizontal when the engine is working at 8 \(\times \)10⁵ W.The resistance to motion of a train is 

The potential energy of a spring when stretched through a distance x is 10J. What is the amount of work done on the same spring to stretch it through on additional distance x?

A man weighing 60 kg climbs up a staircase carrying a load of 20 kg on his head. The stair case has 20 steps each of height 0.2 m. lf he takes 10s to climb, find his power.

When is the exchange of energy maximum during an elastic collision?

Is whole of the kinetic energy lost in any perfectly inelastic collision?

A spark is produced, when two stones are struck against each other. Why?

If energy is neither created nor destroyed, what happens to the so much energy spent against friction?

A man run a distance on the level road. The same man ascends up a hill with the same velocity through the same distance. When does he do more work?

Express a unit of electrical energy in terms of joule.

Two bodies of identical masses with 2^nd body at rest collides with 1^st body, prove that the velocities of the bodies are reversed.

Which is conserved in inelastic collision? Total energy (or) Kinetic energy?

Suppose that the earth revolves around the sun in a perfectly circular orbit. Does the sun do any work on the earth?

A body is displaced 10 \(\hat{j}\)  under the force of \(-2\hat{j}+15\hat{j}+6\hat{i}\ N.\) Calculate the work done.

In some demonstration, a police officer fires a bullet of mass 50.0g with speed 200 ms^-1 on soft plywood of thickness 2.00 cm. The bullet emerges with only 10% of its initial kinetic energy. What is the emergent speed of the bullet?

What is meant by elastic potential energy? Drive an expression for the elastic potential energy of the spring.

Derive an expression for the velocity of the body moving in a vertical circle. And also find a tension at the bottom and the top of the circle.