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Question

The velocity of water wave (v) may depend on their wavelength λ, the density of water ρ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

A
v
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B
v2gλ
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C
v2gλ2
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D
v2g1λ2
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Solution

The correct option is B v2gλ
Let v=kλaρbgc
So, [M0LT1]=La(ML3)b(LT2)c=MbLa3b+cT2c
Applying principle of homogeneity.
b=0,a3b+c=1 and 2c=1
On solving, we get c=12
a=12
vλ12ρ0g12 or v2λg

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