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

We have,

P=El^{2}m^{-5}G^{-2}

E is the energy having dimension ML^{2}T{-2}

m is the mass having dimension [M]

L is the angular momentum having dimension [ML^{2}T^{1}]

G is the gravitational constant having dimension [M^{-1}L^{2}T^{2}]

Substituting the values we get, [P]=[M^{0}L^{0}T^{0}]