Question
The velocity of water waves may depend on their wavelength $\lambda$, the density of water $\rho$ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as(A) $v^{2} \propto \lambda g^{-1} \rho^{-1}$(B) $v^{2} \propto g \lambda$(C) $v^{2} \propto \lambda g \rho$(D) $v^{2} \propto g^{-1} \lambda^{2}$
Step 1
We can write this dependence as $v = k \lambda^{a} g^{b} \rho^{c}$, where $k$ is a dimensionless constant and $a$, $b$, and $c$ are the powers we need to determine. Show more…
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The velocity $v$ of water waves may depend on their wavelength $(\lambda)$, the density of water $(\rho)$ and the acceleration due to gravity $(\mathrm{g})$. The method of dimensions gives the relation between these quantities as (a) $v^{2} \propto \lambda^{-1} \rho^{-1}$ (b) $v^{2} \propto g \lambda$ (c) $v^{2} \propto g \lambda \rho$ (d) $g^{-1} \propto \lambda$
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Round 1
The velocity of water waves $v$ may depend upon their wave length $\lambda$, the density of water $\rho$ and the acceleration due to gravity $g$. The method of dimensions gives the relation between these quantities as (a) $v^{2} \propto \lambda g^{-1} \rho^{-1}$ (b) $v^{2} \propto g \lambda \rho$ (c) $v^{2} \propto g \lambda$ (d) $v^{2} \propto g^{-1} \lambda^{-3}$
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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