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(A) To determine the correct expression,we use dimensional analysis.The dimension of speed $v$ is $[LT^{-1}]$.For option $(A)$,the dimension of $\sqrt

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$\sqrt{g\lambda}$

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(A) To determine the correct expression,we use dimensional analysis.The dimension of speed $v$ is $[LT^{-1}]$.For option $(A)$,the dimension of $\sqrt{g\lambda}$ is $\sqrt{[LT^{-2}] \cdot [L]} = \sqrt{[L^2T^{-2}]} = [LT^{-1}]$,which matches the dimension of speed.For option $(B)$,the dimension of $\sqrt{g/h}$ is $\sqrt{[LT^{-2}] / [L]} = \sqrt{[T^{-2}]} = [T^{-1}]$,which is incorrect.For option $(C)$,the dimension of $\sqrt{\rho gh}$ is $\sqrt{[ML^{-3}] \cdot [LT^{-2}] \cdot [L]} = \sqrt{[MT^{-2}]}$,which is incorrect.For option $(D)$,the dimension of $\sqrt{g/\rho}$ is $\sqrt{[LT^{-2}] / [ML^{-3}]} = \sqrt{[M^{-1}L^4T^{-2}]}$,which is incorrect.Therefore,the only dimensionally consistent expression is $\sqrt{g\lambda}$.

What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

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