Question

Velocity of waves on water is given by $V={kg}^a{\lambda }^b$, where $g$ is acceleration due to gravity, $\lambda$ is wavelength and $k$ is a constant. The values of a and b are:

• A. $-\frac{1}{2},-\frac{1}{2}$
• B. $\frac{1}{2},2$
• C. $2,2$
• D. $\frac{1}{2},\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2},\frac{1}{2}$

$V=k{g}^{\alpha }{\gamma }^b$

$L{T}^{-1}=(L{T}^{-2}{)}^{\alpha }{L}^b$
$L{T}^{-1}=L^{\alpha +b}{T}^{-2\alpha }$
$\alpha +\beta =1$
$-2\alpha =-1$

$\Rightarrow \alpha =\frac{1}{2},\beta =\frac{1}{2}$