The velocity of water waves $$v$$ may depend upon 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 [NCERT 1979; CET 1992; MP PET 2001; UPSEAT 2000]

Question

TuteeHUB · Accepted Answer

$${{v}^{2}}\propto {{g}^{-1}}{{\lambda }^{-3}}$$

TuteeHUB · Answer

$${{v}^{2}}rg$$

TuteeHUB · Answer

$${{v}^{2}}\propto g\lambda \rho $$

TuteeHUB · Answer

$${{v}^{2}}\propto g\lambda $$

1.	The velocity of water waves \[v\] may depend upon 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 [NCERT 1979; CET 1992; MP PET 2001; UPSEAT 2000]
A.	\[{{v}^{2}}rg\]
B.	\[{{v}^{2}}\propto g\lambda \rho \]
C.	\[{{v}^{2}}\propto g\lambda \]
D.	\[{{v}^{2}}\propto {{g}^{-1}}{{\lambda }^{-3}}\]
Answer» D. \[{{v}^{2}}\propto {{g}^{-1}}{{\lambda }^{-3}}\]

The velocity of water waves \[v\] may depend upon 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 [NCERT 1979; CET 1992; MP PET 2001; UPSEAT 2000]

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