Q. The velocity of water waves $\upsilon$ 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) $\upsilon^{2} \propto \lambda g^{- 1}\rho^{- 1}$
B) $\upsilon^{2} \propto g\lambda\rho$
C) $\upsilon^{2} \propto g\lambda$
D) $\upsilon^{2} \propto g^{- 1}\lambda^{- 3}$
Explanation
Let $v^{x} = kg^{y}\lambda^{z}\ \rho^{\delta}$. Now by submitting the dimensions of each quantities and equating the powers of $M,\ L$ and $T$ $we\ get\ \delta = 0\ and\ x = 2,y = 1,z = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.