Question

Someone explain?

Answer 1

Only (A) has units of speed.

Explanation:

Let's start with unit analysis. Considering only the units, we'll write `L` for length and `T` for time, `M` for mass.

`v=L/T, rho = M/L^3, g= L/T^2, h=lambda=L`.

Our choices are all square roots so let's solve for `x` in `v= sqrt{x}`. That's easy, `x = v^2 = L^2/T^2`. So we need to find the radicand with those units.

(A) `g lambda = L/T^2 \times L = L^2/T^2 quad` That one works!

(B) `g/h = (L/T^2)/L = 1/T^2 quad` nope

(C) `rho g h = M/L^3 (L/T^2) L = M/{LT^2} quad` nope

(D) `g/rho = (L/T^2)/1 = L/T^2 quad` nope

So (A).