In an ancient civilization, the unit of length was half of meter, the unit of mass was double the kilogram and the unit of time was half of second. The ratio of   joule and   the new  unit of energy   is _________

Unit of Energy, 1 J $=kg{m}^2{s}^{-2}$ (old unit)

Now, according to question

New unit of mass $=a=2kg$

New unit of length $=b=\frac{1}{2}m$

New unit of time $=c=\frac{1}{2}s$

New unit of energy $=a{b}^2{c}^{-2}$

Ratio $=$$\frac{\text{New unit}}{\text{Old unit}}=\frac{a{b}^2{c}^{-2}}{kg{m}^2{s}^{-2}}=\left(\frac{2kg}{kg}\right){\left(\frac{{\displaystyle \frac{1}{2}}m}{m}\right)}^2{\left(\frac{{\displaystyle \frac{1}{2}}s}{s}\right)}^{-2}=2$