Question

In a new system of units, the units of mass, length, time and current are \(5\,\text{kg}\), \(5\,\text{m}\), \(5\,\text{s}\) and \(5\,\text{A}\), respectively. If \(\mu_0\) and \(\epsilon_0\) are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of \(\sqrt{\mu_0/\epsilon_0}\) is:

Hint:

Identifying that $\sqrt{\mu_0/\epsilon_0}$ has units of Ohms (Resistance) simplifies the dimensional analysis significantly.
Be very careful with negative signs in exponents during substitution; for example, $(1/5)^{-3}$ is $5^3$.
Ensure you use $n_2 = n_1 (\text{ratio})^a$ correctly to find the magnitude in the new system.

Answer 1