Q10DQ - University Physics with Modern Physics

Question

Suppose you chose the fundamental physical quantities to be force, length, and time instead of mass, length, and time. What would be the units of mass in terms of those fundamental quantities?

Step-by-Step Solution

Answer

The unit of mass will be $\frac{{\mathrm{Ns}}^2}{\mathrm{m}}$.

Step 1: Newton’s Second law

A body of mass (m) with acceleration (a) due to a net force (F) acting on it whose magnitude can be calculated as follows-

                                        F = ma

Step 2: Define units of each term in terms of new fundamental quantities.

The new fundamental quantities are force, length, and time. Hence the force has fundamental unit N (Newton), and acceleration has unit $\mathrm{m}/{\mathrm{s}}^2$ . So, the formula for mass is given as-

$\mathrm{m}=\frac{\mathrm{F}}{\mathrm{a}}$ 

Thus, unit of mass is given as-

$$\begin{gathered} \mathrm{kg}=\frac{\mathrm{N}}{{\mathrm{ms}}^{-2}} \\ =\frac{{\mathrm{Ns}}^2}{\mathrm{m}} \end{gathered}$$ 

Therefore, the mass will have a unit of $\frac{{\mathrm{Ns}}^2}{\mathrm{m}}$.