Work, Energy an...

A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin is F (x) = – kx + ax³ . Here, k and a are positive constants. For x ≥ 0, the functional form of the potential energy U_(x) of the particle is

A particle of mass 2 mg moves with constant speed and is found to pass two points 5.0 m apart in a time interval of 5 ms. Find the kinetic energy of the particle

A cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy E₁ and kinetic energy of the second part is E₂, relation between E₁ and E₂ is

A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of 6 ms^-1. The kinetic energy of the larger fragment is

The magnitude of momentum of particle is increased by 100%. The increase in its kinetic energy is

A particle of mass 4m which is at rest explodes into three fragments. Two of the fragments each of mass m are found to move with a speed v each mutually perpendicular directions. The total energy released in this process is

Potential energy of a particle is to α coordinate by equation x² – 2x will be equilibrium at

Two bodies of masses m₁ and m₂ are acted upon by constant force F for a time t. They start from rest and acquire kinetic energies E₁ and E₂, respectively. Then, E₁/E₂ is

A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J. The height at which the kinetic energy of the body becomes half of the original value is