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What is the relationship between height and gravitational potential energy of water behind a dam?
Water is contained in a tidal basin behind a dam. The water has a depth h at high tide and zero at low tide. The gravitational potential energy of the water stored in the basin between a high tide and a low tide is proportional to

1. h^(1/2)
2. h
3. h^2
4. h^3

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Answer:

3. [tex]h^2[/tex]

Explanation:

Energy of volume contained in a dam is given by

[tex]E=\dfrac{1}{2}A\rho gh^2[/tex]

where,

A = Horizontal surface area of the barrage

[tex]\rho[/tex] = Density of water

g = Acceleration due to gravity = 9.81 m/s²

h =  Vertical tidal range,

It can be seen that

[tex]E\propto h^2[/tex]

Hence, the energy is proportional to [tex]h^2[/tex]

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