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

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

  • B

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

  • C

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

  • D

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

Similar Questions

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.

Consider following statements

$(A)$ Any physical quantity have more than one unit

$(B)$ Any physical quantity have only one dimensional formula

$(C)$ More than one physical quantities may have same dimension

$(D)$ We can add and subtract only those expression having same dimension

Number of correct statement is

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The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right) = \frac{{b\theta }}{l}$ Where $P$ is the pressure, $V$ the volume, $\theta $ the absolute temperature and $a$ and $b$ are constants. The dimensional formula of $a$ is

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The quantity $X = \frac{{{\varepsilon _0}LV}}{t}$: ${\varepsilon _0}$ is the permittivity of free space, $L$ is length, $V$ is potential difference and $t$ is time. The dimensions of $X$ are same as that of

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