Physics

# 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:

$\dfrac { 1 }{ 2 },\dfrac { 1 }{ 2 }$

##### SOLUTION

$V=kg^{\alpha }\gamma ^{b}$

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

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Single Correct Medium Published on 18th 08, 2020
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