Question

If the unit of force is $100$ N, unit of length is $10$ m and unit of time is $100$ s, what is the unit of mass in this system of units?

Answer 1

The given units are function of SI units. Therefore, SI unit of mass will also be in terms of kg

Step 1: Write dimension of each quantity.

Dimension of force $\left[F\right]=\left[ML{T}^{-2}\right]=100N\dots \dots \left(i\right)$ Dimension of length $\left[L\right]=\left[L\right]=10m\dots \dots \left(ii\right)$ Dimension of time $\left[t\right]=\left[T\right]=100s\dots \dots \left(iii\right)$

Step 2: Write dimension of each quantity.

Substituting values of [L] and [T] from Eq. (ii) and (iii) in Eq. (i), we get

$x\left[M\right]\times 10\left[L\right]\times \left(100{)}^{-2}\right[T^{-2}]=100[ML{T}^{-2}]$
$\frac{x\times 10}{100\times 100}=100$

$x=100\times 1000kg$
$={10}^5$ kg

Final Answer: The unit of mass in this system will be ${10}^{5}kg$