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 = $10m{s^{ - 1}}$ .
A. $2000{\text{ MJ}}$
B. $200{\text{ MJ}}$
C. $1000{\text{ MJ}}$
D. $500{\text{ MJ}}$

Answer 1

Hint: For Conservation of Energy problems, we have to use the basic formulas of potential energy and Kinetic energy. We have been given the height of the dam, the mass can be calculated by using density and volume. We know the value of acceleration due to gravity and thus we can calculate the value of Potential Energy.

Complete step by step answer:
In the given question we see that the potential energy of the water stored in the dam is at first converted to kinetic energy of the falling water, and then this falling water’s kinetic energy is converted to electrical energy. (Falling water’s kinetic energy rotates the turbines—mechanical energy and the rotating turbine produces electrical energy).
We know potential energy = $mgh$ .Where the respective terms represent mass, acceleration due to gravity and height respectively.

We know that density of water = $1000\,kg/{m^3}$
Given the volume of water = $10000{\text{ }}{m^3}$
Thus, the value of mass is = ${10^7}{\text{ kg}}$
Given height of the dam = $20{\text{ m}}$
Acceleration due to gravity = $10\,ms^{-2}$
Now we will use the formula to calculate the value of potential energy:
Thus, the value of Potential energy = ${10^7} \times 10 \times 20= 2000{\text{ MJ}}$.

Hence, the correct answer is option A.

Note: Thus, we see that these types of problems can be easily solved using the concept of potential energy and using energy conversions. The formula of potential energy and kinetic energy is to be kept in mind and the conversions, from which type to which and where it occurs is to be kept in mind. These types of sums require only a single formula to solve, using potential energy equations.