Physics And Measurement Question 68

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

[NCERT 1979; CET 1992; UPSEAT 2000]

Options:

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}} $

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Answer:

Correct Answer: C

Solution:

Let $ v^{x}=kg^{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 $ .



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