In a system of units where the unit of force is $F=10\text{ N}$, the unit of length is $L=10\text{ m}$, and the unit of time is $T=5\text{ s}$, what is the unit of mass $M$ in this system in kilograms?

Solution

1. The dimension of force is $[F]=[M][L][T{]}^{-2}$.
2. Rearranging for mass, we get $[M]=[F][L{]}^{-1}[T{]}^2$.
3. Substituting the given values, $M=(10\text{ N})\times (10\text{ m}{)}^{-1}\times (5\text{ s}{)}^2$.
4. Calculating the value, $$\begin{array}{rl}M& =10\times 0.1\times 25\\ & =2.5\text{ kg}\end{array}$$.
5. Hence the answer is (A).