The velocity of ripples on water surface depends upon the wavelength $λ$ , density of water d, and acceleration due to gravity g. Which of the following relation is correct among these quantities?

V^{2} \propto g λ

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V^{2} \propto \frac{λ}{g}

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V^{2} \propto \frac{λ}{g d}

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V^{2} \propto g λ d

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Solution

The correct option is A $V^{2} \propto g λ$
$L T^{- 1} = L^{a} {(M L^{- 3})}^{b} {(L T^{- 2})}^{c}$
This gives: $b = 0, c = \frac{1}{2}, a = \frac{1}{2}$
Thus, $v^{2} \propto λ g$

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The velocity of ripples on water surface depends upon the wavelength λ, density of water d, and acceleration due to gravity g. Which of the following relation is correct among these quantities?

The correct option is A V2∝gλLT−1=La(ML−3)b(LT−2)cThis gives: b=0,c=12,a=12Thus, v2∝λg

The velocity of ripples on water surface depends upon the wavelength $λ$ , density of water d, and acceleration due to gravity g. Which of the following relation is correct among these quantities?

The correct option is A $V^{2} \propto g λ$
$L T^{- 1} = L^{a} {(M L^{- 3})}^{b} {(L T^{- 2})}^{c}$
This gives: $b = 0, c = \frac{1}{2}, a = \frac{1}{2}$
Thus, $v^{2} \propto λ g$