Question

In the expression P = E l² m⁻⁵ G⁻², the quantities E, l, m and G denote energy, angular momentum, mass and gravitational constant respectively. Show that P is a dimensionless quantity.

Answer 1

Hii dear,

# PROOF-
Suppose,
P = E.I^2.m^-5.G^-2

Dimensions of P will be given by formula,
[P] = [EI^2M^-5G^-2]

We know,
[E] = [ML^2T^-2]
[G] = [M^-1L^3T-2]
[I] = [ML^2T^-1]

Putting values in eqn.(1),
[P] = [ML^2T^-2][ML^2T^-1]^2[M^-5][M^-1L^3T^-2]^-2
[P] = [ML^2T^-2][M^2L^4T^-2][M^-5][M^2L^-6T^4]
[P] = [M^(1+2-5+2)L(2+4-6)T(-2-2+4)]
[P] = [M^0L^0T^0]

Comparing LHS=RHS,
[P] = null.

Hence, P is dimensionless quantity.

Hope that helps you.

Answer 2

Answer:

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