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
v2∝gλ
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C
v2∝gλ2
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D
v2∝g−1λ2
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Solution
The correct option is Bv2∝gλ Let v=kλaρbgc
So, [M0LT−1]=La(ML−3)b(LT−2)c=MbLa−3b+cT−2c
Applying principle of homogeneity. b=0,a−3b+c=1 and −2c=−1
On solving, we get c=12 ∴a=12 ∴v∝λ12ρ0g12 or v2∝λg