​The value of universal gravitational constant in SI system is G= 6.67*10^-11 Nm^2kg^-2 .What is its value in a new system of units in which unit of distance is 1 km, unit of mass is 10 kg and unit of time is 1 minute?

Dear Student,

Please find below the solution to the asked query:

Given value for the Universal Gravitational constant is 

$G=6.67\times {10}^{-11} N m^2 k{g}^{-2}$

Therefore,

$$\begin{gathered} unit of G=\frac{m^3}{kg-se{c}^2} \\ In new units, \\ G=\frac{{\left({\displaystyle \raisebox{1ex}{$m\text{'}$}\!\left/ \!\raisebox{-1ex}{$1000$}\right.}\right)}^3}{\left({\displaystyle \raisebox{1ex}{$kg\text{'}$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}\right)\left({\displaystyle \raisebox{1ex}{$sec\text{'}$}\!\left/ \!\raisebox{-1ex}{$60$}\right.}\right)}=\frac{m^3}{kg-se{c}^2}\times \frac{600}{{10}^9} \\ \Rightarrow G=6\times {10}^{-7}\times 6.67\times {10}^{-11} \left(In new units\right) \\ \Rightarrow G=40.02\times {10}^{-18} \left(In new units\right) \end{gathered}$$

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