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In the expression P =E L^2 m^(-5) G^(-2)...

In the expression `P =E L^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.

Text Solution

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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.
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