Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Question

Accepted Answer

(1) (√hG)/(c^3/2). [h]=[ML²T⁻¹], [G]=[M⁻¹L³T⁻²], [c]=[LT⁻¹] Idea: multiplying h by G cancels the mass, which is what a pure length needs. [hG]=[ML²T⁻¹][M⁻¹L³T⁻²]=[L⁵T⁻³] [√hG]=[L^5/2T^-3/2] [c^3/2]=[L^3/2T^-3/2] ([L^5/2T^-3/2])/([L^3/2T^-3/2])=[L] This combination is the Planck length.

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Step-by-step solution

Why the other options are wrong