Question

In a parallel universe, parallel physicists on a parallel Earth picked units of time T], mass [M] and charge [C as their basic three dimensions for their physics. Express units of length in terms of these three basic units.

Answer 1

Answer:

$L = \frac{M}{C*T}$

Explanation:

In our universe the unit of current used to be defined as the current that produces a certain force per unit of length between two wires separated by a certain length. This means:

$I = \frac{F}{l * l}$

Replacing force by its definition

$I = \frac{M * \frac{l}{T^2}}{l^2} = \frac{M}{l * T^2}$

And since current is charge over time

$C = I * T$

$C = \frac{M}{l * T}$

From this we can define length as a function of time, mass, and charge:

$L = \frac{M}{C*T}$