In a hydroelectric power plant, water falls at a rate of $1000 k g s^{- 1}$ from a height of $100 m$ . Assuming that 50% of the energy of falling water is converted into electrical energy, calculate the power generated. (Take $g = 10 m s^{- 2}$ )

$500 k W$

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$495 k W$

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$490 k W$

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$480 k W$

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Solution

The correct option is A
$500 k W$

Mass of water, $m = 1000 k g$
Height, $h = 100 m$ , acceleration due to gravity, $g = 10 m s^{- 2}$
Energy possessed by water = Potential energy = $m g h$ = $1000 \times 10 \times 100 = 10^{6} J$
It is mentioned that only 50% of the energy is converted into electrical energy.
So, the amount of Electrical energy generated $= Total Energy \times \frac{50}{100} = 5 \times 10^{5} J$
Time taken is $1 s$ , we know that the power generated = $\frac{E n e r g y}{T i m e}$ = $500 k W$ .

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In a hydroelectric power plant, water falls at a rate of $1000 k g s^{- 1}$ from a height of $100 m$ . Assuming that 50% of the energy of falling water is converted into electrical energy, calculate the power generated. (Take $g = 10 m s^{- 2}$ )

Q. Question 13
In a hydroelectric power plant more electrical power can be generated if water falls from a greater height because

(a) its temperature increases
(b) larger amount of potential energy is converted into kinetic energy
(c) the electricity content of water increases with height
(d) more water molecules dissociate into ions

Assertion: The amount of electric power generated in hydroelectric power plant A is more than that of hydroelectric power plant B.
Reason: The potential energy possessed by the stored water is converted into electricity.

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g

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In a hydroelectric power plant, water falls at a rate of 1000 kg s−1 from a height of 100 m. Assuming that 50% of the energy of falling water is converted into electrical energy, calculate the power generated. (Take g=10 ms−2)

In a hydroelectric power plant, water falls at a rate of $1000 k g s^{- 1}$ from a height of $100 m$ . Assuming that 50% of the energy of falling water is converted into electrical energy, calculate the power generated. (Take $g = 10 m s^{- 2}$ )