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

`P=EL^(2)m^(-5)G^(-2)`
Energy (E) `=[ML^(2)T^(-2)]`
Angular momentum `(L)=ML^(2)T^(-1)`
Mass = [M]
Universal gravitational constant
`(G)=[M^(-1)L^(3)T^(-2)]`
`P=[ML^(2)T^(-2)][ML^(2)T^(1)]^(2)[M]^(-5)[M^(-1)L^(3)T^(-2)]^(-2)`
`P=M^(1+2+5+2)L^(2+4-6)T^(-2-2+4)`
`P=[M^(0)L^(0)T^(0)]`
Hence P is dimensional less quantity.