Question

If the value of universal gravitational constant in SI unit is $6.6\times {10}^{-11}N{m}^2/k{g}^2$. Then find its value in CGS system.

Answer 1

$1$ Netwon $=1$kg $m{s}^{-2}$

Hence $N{m}^2/k{g}^2=\frac{kgm{s}^{-2}\times m^2}{k{g}^2}$$=k{g}^{-1}{m}^3{s}^{-2}$

$1$kg$={10}^3$grm

$1$m$={10}^2$cm

$\therefore$ $k{g}^{-1}{m}^3{s}^{-2}=\frac{({10}^3{)}^{-1}\times ({10}^2{)}^3}{s^{-1}}$

$=\frac{{10}^{-3}\times g{m}^{-1}\times {10}^{6}c{m}^3}{s^2}$

$\therefore 1N{m}^2/k{g}^2=k{g}^{-1}{m}^3{s}^{-2}={10}^{3}gr{m}^{-1}c{m}^3{s}^{-2}$

$G=6.6\times {10}^{-11}\times 10^{3}gr{m}^{-1}c{m}^3{s}^{-2}$

$\therefore G=6.67\times {10}^{-8}gr{m}^{-1}c{m}^3{s}^{-2}$.