JEE Mains Model Paper 13

The relation written by the boy m =

m0

(1−v2)1∕2

According to the principle of homogeneity of dimensions, the dimensions on either side of arelation must be same i.e., the powers of M, L, T on either side of a relation must be same.
Dimension of m is equal to the dimension of m0, therefore the denominator (1−v2)1∕2 should b dimensionless. In denominator 1 is dimensionless but factor v2 is notdimensionless. To make it dimensionless we have to divide it by the same physical quantitywith same power, therefore it should be v2∕c2, to become dimensionless.
Hence, the correct relation should be m =

m0

(1− v2 C2 )1∕2