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. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:

m = m_o/(1-v²)^1/2

Answer 1

The given formula will be dimensionally correct only when the dimension of L.H.S is the same as that of R.H.S.
This is only possible when the factor, (1 − v²)^1/2 is dimensionless i.e., (1 – v²) is dimensionless. This is only possible if v² is divided by c². Hence, the correct relation is

m = m_o/(1-v²)^1/2