Q. Show Mass energy Relation?

Until the time of Einstein, mass and energy were considered as two different physical quantities. But in 1905, with the help of postulates of the special theory of relativity Einstein demonstrated that neither mass nor energy were conserved separately, but they could be traded one for the other and neither mass nor energy were conserved separately, but they could be traded one for the other and only the "total mass energy" was conserved. The most famous relationship between the mass and the energy given by Einstein is

E = mc²

Here m is the effective mass, c is the speed of light, and E is the energy equivalent of the mass. According to this relation a certain amount of energy of any form can be considered as mass or conversely. Energy will increase if mass decreases; mass can be turned into energy. If the mass increases, energy must be turned into energy. If the mass increases, energy must be supplied, energy can be turned into mass. Mass and energy are interchangeable. Mass and energy is the same thing. According to Einstein's first postulate of relativity, all laws related with physical events have the same form in all inertial frames. Thus Newton's second law and work energy theorem will also remain valid in all inertial frames.

F = dp / dt = dp (mv) /dt

Now from the statement of work energy theorem

Change in kinetic energy = work done by the particle

D E_k = dW = Fdx