Someone explain?

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1 Answer
Apr 25, 2018

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).