Question

The velocity v of water waves may depend on their
wavelenght (a), the density of water (p) and the acceleration
due to gravity(g). The method of dimensions gives the
relation between these quantities as​

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Physics

Units and Measurement

Dimensions and Dimensional Analysis

The velocity of water waves...

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Asked on December 20, 2019 by

Peru Mishra

The velocity of water waves (v) may depend on their wavelength

′

λ

′

, density of water 'p' and acceleration due to gravity 'g'. The method of dimensions gives the relation between these quantities as

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ANSWER

Dimension of Velocity is LT

−1

Dimension of wavelength λ is L

Dimension of acceleration due to gravity g is LT

−2

Dimension of Density of water ρ is ML

−3

Let v∝λ

a

g

b

ρ

c

Using Dimensional method:

a+b−3c=1 ( Length )

c=0 ( Mass )

−2b=−1 ( Time )

b=0.5

Hence, a=0.5

∴v∝

gλ

v

2

∝gλ