Question

Convert gravitational constant (G) from CGS to MKS system.

Answer 1

The dimensional formula of G is
$\left[M^{-1}{L}^3{T}^{-2}\right]$, i.e., $a=-1,b=3,c=-2$

SI system	CGS system
$M_1=1kg$	$M_2=1g$
$L_1=1m$	$L_2=1cm$
$T_1=1s$	$T_2=1s$

By using $n_2=n_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$

Value of G in CGS unit
= $6.67\times {10}^{-8}c{m}^{3}g{s}^{-2}$

= $6.67\times {10}^{-8}{\left[\frac{g}{kg}\right]}^{-1}{\left[\frac{cm}{m}\right]}^3{\left[\frac{s}{s}\right]}^{-2}$

=$6.67\times {10}^{-8}{\left[\frac{g}{{10}^{3}g}\right]}^{-1}{\left[\frac{cm}{{10}^{2}cm}\right]}^3{\left[\frac{s}{s}\right]}^{-2}$
=$6.67\times {10}^{-11}$
$\therefore G=6.67\times {10}^{-11}$ MKS units.