Question

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

• A. $500kW$
• B. $495kW$
• C. $490kW$
• D. $480kW$

Answer 1

The correct option is A

$500kW$

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