A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ 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 = m०/(1/v²)½ Guess where to put the missing c.
According to the principle of homogeneity of dimensions, powers of M, L, T on either side of the formula must be equal. For this, on RHS, the denominator (1−v 2 ) 1/2 should be dimensionless. Therefore, instead of (1−v 2 ) 1/2 ,we should write (1−v 2 /c 2 ) 1/2 . Hence, the correct formula would be m= (1−v 2 /c 2 ) 1/2 m 0
