In the expression P = El ^2 ~m ⁻⁵ G ⁻² where E , 1, ~m and G represent Energy, Angular Momentum, Mass and Gravitational Constant, the dimensions of P are

Step-by-step solution

The dimensions of the given physical quantities are as follows: Energy (E) = [M^1 L^2 T⁻²] Angular Momentum (l) = [M^1 L^2 T⁻¹] Mass (m) = [M^1] Gravitational Constant (G): From F = G m₁ m₂ r^2 , we have G = F r^2 m^2 = [M^1 L^1 T⁻²] [L^2] [M^2] = [M⁻¹ L^3 T⁻²] Now, substitute these dimensions into the expression P = E l^2 m⁻⁵ G⁻² : P = [M^1 L^2 T⁻²] ([M^1 L^2 T⁻¹])^2 ([M^1])⁻⁵ ([M⁻¹ L^3 T⁻²])⁻² P = [M^1 L^2 T⁻²] [M^2 L^4 T⁻²] [M⁻⁵] [M^2 L⁻⁶ T^4] Combine the powers of M, L, and T: M: 1 + 2 - 5 + 2 = 0 L: 2 + 4 + 0