In the expression `P=Et^2m^-5G^-2` the quantities E,I,m and G denote energy , angular momentum, mass and gravitational constant respectively. Show that P is a dimensionless quantity.

Explanation

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 .