question_answer 70)

                  In the expression \[P=\text{ }E{{l}^{2}}\,\,{{m}^{-5}}{{G}^{-2}},\text{ }m,\text{ }l\] and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.                

Answer:

                  As                 \[[P]=[M{{L}^{2}}{{T}^{-2}}]\,{{[M{{L}^{2}}{{T}^{-1}}]}^{2}}{{[M]}^{-5}}{{[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]}^{-2}}\]                 \[=[{{M}^{0}}{{L}^{0}}{{T}^{0}}],\]                 P is a dimensionless quantity.