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}} $
Show Answer
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 $ .
