question_answer

Calculate the dimensions of universal gravitational constant If its value in SI units is \[6.67\times {{10}^{-8}}g\,c{{m}^{3}}{{s}^{-2}}\], what will be its value in cgs system?

Answer:

                From     \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\] \[G=\frac{F{{r}^{2}}}{{{m}_{1}}{{m}_{2}}}=\frac{\left( ML{{T}^{-2}} \right)\left( {{L}^{2}} \right)}{{{M}^{2}}}=\left[ {{M}^{-1}}{{L}^{3}}{{T}^{-2}} \right]\] \[G=6.67\times {{10}^{11}}k{{g}^{-1}}{{m}^{3}}{{s}^{-2}}=6.67\times {{10}^{-11}}{{\left( {{10}^{3}}g \right)}^{-1}}{{\left( {{10}^{2}}cm \right)}^{3}}{{s}^{-2}}=6.67\times {{10}^{-8}}gc{{m}^{3}}{{s}^{-2}}\].