Question

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

• 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 1

The correct option is C

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

$Let{v}^x=k{g}^y{\lambda }^z{\rho }^{\delta }$

Now by substituting the dimensions of each quantities and equating the powers of M,L and T, we get $\delta$ = 0 and x = 2,y = 1,z = 1.