Find the value of $100 J$ on a system which has $20 cm$, $250 g$ and half minute as fundamental units of length, mass and time.

Hint : Dimensions are actual quantities that can be estimated, whereas units are random names that connect to particular dimensions to execute it relative All units for the identical dimension are linked to each other through a conversion factor.

Complete step-by-step solution:
As we know, joule is a unit of work.
Dimensions of joule is $[M L^{2} T^{-2}]$
Here, $a = 1; b = 2; c = -2$
To convert, SI unit to another system.
$M_{1} = 1Kg = 1000 ; M_{2} = 250 g$
$T_{1} = 1s; T_{2} = \dfrac{1}{2} min = 30 s$
$L_{1} = 1m; L_{2} = 20 cm = 0.2m$
$n_{1} = 100 J; n_{2} = ?$
$n_{2} = n_{1} \left( \dfrac{M_{1}}{M_{2}} \right)^{a} \left( \dfrac{L_{1}}{L_{2}} \right)^{b} \left( \dfrac{T_{1}}{T_{2}} \right)^{c}$
Put all the values in the above formula.
$n_{2} = 100 \left( \dfrac{1000}{250} \right)^{1} \left( \dfrac{1}{0.2} \right)^{2} \left( \dfrac{1}{30} \right)^{-2}$
$n_{2} = 100 \times 4 \times 25 \times 900$
$n_{2} = 9 \times 10^{6} $new units.

Note: We generally choose length, mass, time, and temperature as basic dimensions. This gives the force a function of length, mass, and time. Others set force as one of their standard dimensions and determine mass by dividing them by acceleration due to gravity.