[AdiDex]

While plotting  of maxwell distribution of speed , on y axis we take fraction of molecules having speed u .
Then why define it as  1/N*dN/du ?? Fractions are dimensionless but it has dimension of [LT]^-1 ??
only dN/N should be present there .

[mjc123]

Because it is a continuous distribution, the fraction with speed equal to exactly u is zero. It is defined so that the fraction with speeds between u and u+du is equal to f(u)du. From this it follows that
f(u) = 1/N_t dN/du, as f(u)du = 1/N_t dN/du du = 1/N_t*dN(u u+du)
where N_t is the total number of molecules (constant) and N is a variable.
f(u) has the dimensions of 1/speed, i.e. [LT^-1]^-1