Someone explain?

enter image source here

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).