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From Work-Energy theorem, the kinetic energy of a moving body is equal to the work done by the external force that imparts the velocity to the body at rest. If ‘F’ is the force acting on the body, the work done by the force on the body in raising its velocity from v = 0 to v = ‘v’ is given by :
Kinetic energy of the body,
But from the relation of variation of mass with velocity, the mass of body in motion is
where m0, being rest mass of body.
Therefore, Ek becomes
Thus the kinetic energy for a moving body is equal to ‘gain in mass’ times the square of speed of light. Then total energy (E) of the body is the sum of rest energy and kinetic energy of the body. That is,
E = Rest energy + Relativistic kinetic energy
Which is better known as Einstein’s mass-energy relation who states a universal equivalence between mass and energy?