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Q.

The velocity of water waves may depend on their wavelength l, the density of water r and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

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a

$v^{2} \infty λ g^{- 1} ρ^{- 1}$

b

$v^{2} \infty g λ$

c

$v^{2} \infty λ g ρ$

d

$v^{2} \infty g^{- 1} λ^{2}$

answer is B.

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Detailed Solution

$L T^{- 1} = {[L]}^{x} {[M L^{- 3}]}^{y} {[L T^{- 2}]}^{z}$

$solving we get x = \frac{1}{2}, y = 0 and z = \frac{1}{2} v = \sqrt{g λ}$

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