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If E, M, L and G denote energy, mass, an...

If `E, M, L and G` denote energy, mass, angular momentum and gravitational constant respectively, then the quantity `(E^(2)L^(2)//M^(5)G^(2))` has the dimensions of

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Taking dimensional formulac energy `( E)= ML^(2)T^(-2)`
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^(502)L^(0+6)T^(0-4))`
= A dimensionless quantity .
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