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 Gr

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.