Question

The speed of waves on the surface of the ocean is supposed to depend at most on the density of the water $\rho$, the gravitational field strength (or gravitational acceleration) $g$ and the wavelength of the waves $\lambda$. The speed of ocean waves is then expected to be proportional to:

• A. $\sqrt{\rho g\lambda }$
• B. $\sqrt{g\lambda }$
• C. $\sqrt{g\lambda /\rho }$
• D. $\sqrt{g/\lambda }$

Answer 1

The correct option is B $\sqrt{g\lambda }$

Dimension of $g$ is $L{T}^{-2}$ and that of $\lambda$ is $L$

Thus $\sqrt{g\lambda }$ has the dimensions as $L{T}^{-1}$ which is same as that of velocity.

So, the speed of ocean waves is expected to be proportional to $\sqrt{g\lambda }$