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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 repectively then the quantity `(E^(2)L^(2)//M^(5)G^(2))` has the dimensions of :-

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Taking dimensional formulae
energy (E) = `mL^2 T^(-2)`
mass (M) `= ML^(0)T^(-1)`
Universal Gravitational constant
(G)= `M^(-1)L^(-3)T^(-2)`
Substituting in `(EL^2)/(M^5G^2) `, we get
`((ML^2 T^(-2))(ML^2 T^(-1))^2)/((ML^0T^0)(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 dimensionaless quantity .
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