1. Tardigrade
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  3. Physics
  4. The velocity of water waves v may depend upon their wavelength λ , the density of water ρ and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

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Q. 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

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

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 $x = 2 , \, y = 1 , \, z = 1$ .