In the expression P = E l2 m–5 G–2, E, m
Question:

In the expression P = E l2 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.

Solution:

From the problem, P = E l2 m–5 G–2

E is the energy = [ML2T-2]

m is the mass = [M]

L is the angular momentum = [ML2T1]

G is the gravitational constant = [M-1L2T2]

Substituting the values we get, [P] = [M0L0T0]