Question

The height of water in a dam reduces by $20m$, which is used to generate electricity. The water further fell by $10m$ 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 $g=10m{s}^{-2}$.

• A. 2000 MJ
• B. 200 MJ
• C. 1000 MJ
• D. 500 MJ

Answer 1

The correct option is A 2000 MJ

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