Il the velocity v of water waves
may depend on their wavelength
density of water p and the acceleration
due to grauity g. Find relation between
these quantities by the method of
dimension
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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
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