If E, M, L and G denote energy, mass, angular momentum and universal Gravitational constant respectively, prove that (EL^(2))/(M^(5)G^(2)) is a dimensionless quantity.

If E, M, L and G denote energy, mass, angular momentum and universal G

1.	If E, M, L and G denote energy, mass, angular momentum and universal Gravitational constant respectively, prove that (EL^(2))/(M^(5)G^(2)) is a dimensionless quantity.
Answer» Solution :Taking dimensional formulae energy `(E )= ML^(2)T^(-2)` mass (M) `= ML^(0) T^(0)` ANGULAR Momentum `(L)= ML^(2)T^(-1)` Universal GRAVITATIONAL constant `(G )= M^(-1) L^(3) T^(-2)` Substituting in `(EL^(2))/(M^(5)G^(2))`, we get `((ML^(2)T^(-2))(ML^(2)T^(-1))^(2))/((ML^(0)T^(0))^(5)(M^(-1)L^(3)T^(-2))^(2))= (M^(1+2)L^(2+4)T^(-2-2))/(M^(5-2)L^(0+6)T^(0-4))` = A dimensionless quantity.