Question

A famous relation in Physics relates moving mass m to the rest mass `m_0` of a particle in terms of its speed `upsilon` and the sped of light c. (This relaiton first arose as a consequence of special theory of relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes `m = (m_0)/((1 - upsilon^2)^(1//2)`Guess where to put the missing c?

Answer 1

According to the principle of homogeneity of dimensions, powers of M, L, T on either side of the forumal
must be equal. For this on RHS, the denominator `(1 - upsilon^2)^(1//2)` should be dimensionless. Therefore instead
of `(1 -upsilon^2)^(1//2)`, we should write `(1 - upsilon^2//c^2)^(1//2)`
Hence, the correct formula would be `m = (m_0)/((1 -upsilon^2//c^2)^(1//2)`