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In the expression P =E L^2 m^(-5) G^(-2)...

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

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To show that \( P = E L^2 m^{-5} G^{-2} \) is a dimensionless quantity, we need to analyze the dimensions of each component in the expression. ### Step 1: Identify the dimensional formulas 1. **Energy (E)**: The dimensional formula for energy is given by: \[ [E] = [M][L^2][T^{-2}] \] where \( M \) is mass, \( L \) is length, and \( T \) is time. ...
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