According to law of conservation of energy, energy changes from one form to another form, but the total energy of that system

Options

A. increases
B. decreases
C. alternates
D. remains the same

Answer

**Step-by-Step Solution:**

1. **Understanding the Law of Conservation of Energy**: The law states that energy cannot be created or destroyed; it can only change from one form to another. This means that the total energy in a closed system remains constant.

2. **Identifying Energy Forms**: In the example provided, we have a body at a height (stage 1) which possesses potential energy due to its position. As the body moves downward (stage 2), this potential energy is converted into kinetic energy as the body gains speed.

3. **Calculating Energy at Stage 1**: At stage 1, the energy of the body is purely potential energy (PE). The formula for potential energy is given by:
\[ PE = mgh \]
where \( m \) is the mass, \( g \) is the acceleration due to gravity, and \( h \) is the height.

4. **Calculating Energy at Stage 2**: At stage 2, as the body moves down, it has kinetic energy (KE). The formula for kinetic energy is:
\[ KE = \frac{1}{2} mv^2 \]
where \( v \) is the velocity of the body at this stage.

5. **Comparing Energies**: According to the law of conservation of energy, the total energy at stage 1 (potential energy) should equal the total energy at stage 2 (kinetic energy). Therefore, we can write:
\[ mgh = \frac{1}{2} mv^2 \]
This equation shows that the total energy remains constant, even though it changes forms.

6. **Conclusion**: The total energy of the system does not increase or decrease; it remains the same as energy changes from potential to kinetic. Thus, the correct answer to the question is that the total energy of the system remains the same.

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