Question

the velocity v of water waves depends on the wavelength lambda density of water and acceleration due to gravity g using method of deimensions. find the formula for velocity

Answer 1

Answer:

∝gλ

Explanation:

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