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?

The correct option is 10⁵ kg.

To find the unit of mass in the new system of units, we can use the relation between force, mass, length, and time from dimensional analysis.
The dimensional formula for force ($F$) is given by:
$\left[F\right]=\left[M\right]\left[L\right]{\left[T\right]}^{-2}$

Here, $M$ represents mass, $L$ represents length, and $T$ represents time. We can rearrange this formula to solve for the unit of mass ($M$):
$\left[M\right]=\frac{\left[F\right]}{\left[L\right]{\left[T\right]}^{-2}}=\frac{\left[F\right]{\left[T\right]}^2}{\left[L\right]}$

Now, let's substitute the values given for the units in the new system:
Unit of force, $\left[F\right]=100\text{N}$
Unit of length, $\left[L\right]=10\text{m}$
Unit of time, $\left[T\right]=100\text{s}$

Substituting these values into our rearranged equation:
$\left[M\right]=\frac{100\times {\left(100\right)}^2}{10}\text{kg}$

Simplifying the mathematical expression:
$\left[M\right]=\frac{100\times 10000}{10}\text{kg}$
$\left[M\right]=\frac{1000000}{10}\text{kg}$
$\left[M\right]=100000\text{kg}$
$\left[M\right]={10}^5\text{kg}$

Thus, the unit of mass in this system of units is 10⁵ kg.