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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.
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Solution
Dimensional formulas of E, l and G:
E = [ML2T–2]
l = [ML2T–1]
G = [M–1L3T–2]
∴ Dimension of P = El2m–5G–2:
[P] = `([E] [l^2])/([M^5][G^2])`
= `([ML^2T^-2] [ML^2T^-1]^2)/([M]^5[M^-1L^3T^-2]^2`
= `[M^0L^0T^0]`
So, P is a dimensionless quantity.
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