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the velocity v of water waves may depend on their wavelength density of water and acceration due to gravity find the relation between these quantity by the method of dimension.

Answer 1

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Answer 2

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Step-by-step explanation:

v = k λ g h

$we \ know \ dimension \ of \ velocity=[M^{0} L^{1} T^{-1}] \\\\Length=[L^{1} ] \ Gravity=[L^{1} T^{-2}] \ and \ Density=[M^{1} L^{-3} ]\\ \\Now \ putting \ all \ value$$[L^{1} T^{-1}]=[L^{a} ][(L^{1} T^{-2})^{b}][{(M^{1} L^{-3} })^{c}]\\\\we \ get \ c=0\\\\b=\frac{1}{2} \ and \ a=\frac{1}{2}$

so v = k √λg

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