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  • In the expression P=E\; I^{2}m^{-5}G^{-2},E,m,I\; and\; G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

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

Answers (1)

The dimensional formula of –

E=[ML^{2}T^{-2}]

I=[ML^{2}T^{-1}]

G=[M^{-1}L^{3}T^{-2}]

Now let us find out the dimension of P

P=EI^{2}m^{-5}G^{-2}

[P]=\frac{[E][I^{2}]}{[m^{5}][G^{2}]}

        =\frac{[ML^{2}T^{-2}][ML^{2}T^{-1}]^{2}}{[M]^{5}[M^{-1}L{3}T^{-2}]^{2}}

        \ \ =\frac{M^3L^{6}T^{-4}}{M^3L^{6}T^{-4}}

         =[M^{0}L^{0}T^{0}]

Hence, it is clear that P is a dimensionless quantity.

Posted by

infoexpert22

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