Question

A famous relation in physics relates 'moving mass' m to the 'rest mass' m₀ of a particle in terms of its speed v and the speed of light c. A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:

m = m₀/(1-v²)^1/2 Guess where to put the missing 'c'.

Answer 1

On rearranging, we have m₀/m =√(1-v²).

Since, the left hand side is dimensionless, so the right hand side should also be dimensionless.This will be so,if √(1-v²) is √(1 -v²/c²).