What is the famous relation in physics which relates 'moving mass' m to the ' rest mass ' $m_{0}$ of particle in terms of its speed v and the speed of light c. (this relation first arose as a consequence of special relativity)

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Solution

We know that,

$\frac{m_{0}}{m} = \sqrt{1 - v^{2}}$

Left hand side is dimensionless.

Therefore, right hand side should also be dimensionless

If is possible only when $\sqrt{1 - v^{2}}$ should be $\sqrt{1 - \frac{v^{2}}{c^{2}}}$

Thus, the correct formula is

$m = m_{0} {(1 - \frac{v^{2}}{c^{2}})}^{- \frac{1}{2}}$

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What is the famous relation in physics which relates 'moving mass' m to the ' rest mass ' m0 of particle in terms of its speed v and the speed of light c. (this relation first arose as a consequence of special relativity)

We know that, m0m=√1−v2 Left hand side is dimensionless. Therefore, right hand side should also be dimensionless If is possible only when √1−v2 should be √1−v2c2 Thus, the correct formula is m=m0(1−v2c2)−12

What is the famous relation in physics which relates 'moving mass' m to the ' rest mass ' $m_{0}$ of particle in terms of its speed v and the speed of light c. (this relation first arose as a consequence of special relativity)