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Monday, April 6, 2020

Which formula could be correct for the speed v of ocean waves in terms of the density ρ of seawater, the acceleration of free fall g, the depth h of the ocean and the wavelength λ?


Question 14
Which formula could be correct for the speed v of ocean waves in terms of the density ρ of seawater, the acceleration of free fall g, the depth h of the ocean and the wavelength λ?
A v = gλ                     B v = √(g/h)                 C v = √(ρgh)                D v = √(g/ρ)





Reference: Past Exam Paper – June 2007 Paper 1 Q3





Solution:
Answer: A.

Unit of velocity: m s-1

Consider the overall unit of the options provided.

The unit of the correct option should have the units of velocity.


Note that square root means ‘a power/index of ½ or 0.5’.


Unit of √(gλ): [ms-2 m]0.5 = [m2s-2]0.5 = m s-1 

Unit of √(g/h): [ms-2 m-1]0.5 = [s-2]0.5 = s-1

Unit of √(ρgh): [kgm-3 ms-2 m]0.5 = [kg m-1 s-2]0.5 = kg0.5 m-0.5 s-1

Unit of √(g/ρ): [ms-2 kg-1m3]0.5 = [m4 s-2 kg-1]0.5 = m2 s-1 kg-0.5

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