The velocity of water waves may depend on their wavelength, the density of water and the acceleratio

Question

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

Professor PC Thomas Classes · Answer

DF of $\mathrm{LHS}=\mathrm{L}^{2} \mathrm{~T}^{-2}$ Check each alternative\ a) $\mathrm{g}^{-1} \lambda^{-1}=\left(\mathrm{LT}^{-2}ight)^{-1}(\mathrm{~L})^{-1}=\mathrm{L}^{-2} \mathrm{~T}^{2}$\ b) $\mathrm{g} \lambda=\left(\mathrm{LT}^{-2}ight) \mathrm{L}=\mathrm{L}^{2} \mathrm{~T}^{-2}$\