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 theory of relatively
given by Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant
c. He writes m=m0(1−v2)12. Guess where to put the missing c?
Dimension of L.H.S. should be equal to R.H.S.
m=m0(1−v2)12
L.H.S. = [M]
R.H.S. we already have m0 whose dimension will be [M]
So denominator should be dimensionless
Denominator is (1−v2)
1 is dimensionless
But v has dimension [LT]
Also c has same dimension
⇒v2c2 will be dimensionless
m=m0[1−(VC)2]12