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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