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:


ANSWER

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


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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