Question

In a new system of units, the unit of mass is $100g$, unit of length is $4m$ and unit of time is $2s$. Find the numerical value of $10J$ in this system.

Answer 1

Given, unit of mass $=100g$ Unit of length $=4m$ Unit of time$=2s$ Then numerical value for $10J$,
$n_2=n_1{\left[\frac{M_1}{M_2}\right]}^1{\left[\frac{L_1}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^{-2}$
$n_2=10{\left(\frac{kg}{100g}\right)}^1{\left(\frac{m}{4m}\right)}^2{\left(\frac{s}{2s}\right)}^{-2}$
$n_2=10{\left(\frac{1000g}{100g}\right)}^1{\left(\frac{m}{4m}\right)}^2{\left(\frac{s}{2s}\right)}^{-2}$
$n_2=25$
Final answer: $25$