Question

What formula could be correct for the speed "v" of ocean waves in terms of the density "p" of sea water, the acceleration of free fall "g", the depth of the ocean and the wavelength "y" ?

Answer 1

Choices Please. I remember seeing this question somewhere. As far as my memory goes, I solved by dimensional analysis of the given options

Answer 2

Sure thing.

Answer 3

He he. Give me the complete question and I give you the sure answer

Answer 4

with choices

Answer 5

\[A) v=\sqrt{gy} \]

Answer 6

\[ B) v=\sqrt{g/h} \]

Answer 7

\[C) v= \sqrt{pgh}\]

Answer 8

\[D) v=\sqrt{g/p}\]

Answer 9

I would also appreciate an explanation :)

Answer 10

Yes The option A is correct. Just remembered it now and yes I got it dimensional analysis

Answer 11

How so?

Answer 12

Wavelength(lamba) --> m
g-->ms^(-2)

\[\sqrt{gy} \]
\[\sqrt{ms^{-2}m} \]
\[\sqrt{m^2s^{-2}}\]
\[ms^{-1}\]
which is the unit of velocity. Try with rest of the options.It won't work :D

Answer 13

It won't work means "It won't give dimensions as ms^(-1)"

Answer 14

Ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
That was so simple. Idk maybe I had a mindblock... too much physics ahhh!

Answer 15

No problem. Make sure you eliminate options via Dimensional analysis if your brain is not working for a problem

Answer 16

Right, thanks!

Answer 17

Welcome :D