The Total solution for NCERT class 6-12
A famous relation in physics relates ‘moving mass’ m tothe ‘rest mass’ m0 of a particle in terms ofits speed v and the speed of light, c. (Thisrelation first arose as a consequence of special relativity due to AlbertEinstein). A boy recalls the relation almost correctly but forgets where to putthe constant c. He writes:
Given the relation,
Dimension of m = M1 L0 T0
Dimension of = M1 L0 T0
Dimension of v = M0 L1 T–1
Dimension of v2 = M0 L2 T–2
Dimension of c = M0 L1 T–1
Thegiven formula will be dimensionally correct only when the dimension of L.H.S isthe same as that of R.H.S. This is only possible when the factor, is dimensionless i.e., (1 – v2) isdimensionless. This is only possible if v2 isdivided by c2. Hence, the correct relation is
.