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Derive the formula $E=mc^2$ from the standard equation of kinetic energy?

Indian Institute of Science Education and Research > Physics > sem 2 > Classical Mechanics

Mark : 20M

Year: April 2015

We have the standard equation of kinetic energy $$E=\displaystyle\frac{1}{2}mv^2$$ Devide both side of the equation by $c^2$ . Thus we get $\frac{E}{c^2}=\frac{1}{2}m\frac{v^2}{c^2}$
And we have the formula $$v= \frac{v_0}{\sqrt{1-\frac{v^2}{c^2}}}$$
Again with some basic algebra skill we can get $$E=\frac{1}{2}m\frac{v^2-v_0^2}{v_0^2}c^2$$
Since the value of $\frac{1}{2}\frac{v^2-v_0^2}{v_0^2}$ is very small that can be neglected and finally resulting into the most famous equation of all time $$E=mc^2$$