Tag: energy transformations and energy transfers

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Multiple choice physics the essence of change different forms of energy energy conversions energy transformations and energy transfers

The height of water in a dam reduces by $20  m$, which is used to generate electricity. The water further fell by $10  m$ into the tunnel to strike the turbine plates. If the volume of water is ${10}^{4}  {m}^{3}$, find the hydel energy generated. Assume all the potential energy of the water being converted into electricity. Take $g = 10  m{s}^{-2}$.

  1. 2000 MJ

  2. 200 MJ

  3. 1000 MJ

  4. 500 MJ
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A Correct answer
Explanation

The potential energy of the stored water is converted into kinetic energy which is then converted into electrical energy.
The potential energy of water $= mgh$        ...... (1)
The volume of water $= 10000  {m}^{3}$.
The mass of water $=$ volume $\times$ density $= 10000 \times 1000 = {10}^{7}  kg$.
Also, the depth of water $= 20  m$.
$\therefore$ The height of CG of stored water $= 10  m$.
The total height through which water falls $= 20  m$.
Substituting it in (1), we get potential energy of water $= {10}^{7} \times 20 \times 10 = 2000  MJ$.