A body has a free fall from a height of 20 m. After falling through a distance of 5 m, the body would

Options

A. lose one-fourth of its total energy
B. lose one-fourth of its potential energy
C. gain one-fourth of its potential energy
D. gain three-fourth of its total energy

Explanation

To solve the problem, we need to analyze the potential energy of the body at two different heights during its free fall.

### Step 1: Understand the concept of potential energy
Potential energy (PE) is the energy possessed by an object due to its position in a gravitational field. It can be calculated using the formula:
\[ PE = mgh \]
where:
- \( m \) = mass of the body (in kg)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height above the reference point (in meters)

### Step 2: Calculate the potential energy at the initial height (20 m)
At the initial height of 20 m, the potential energy (PE_initial) can be expressed as:
\[ PE_{\text{initial}} = mg \times 20 \]
This represents the total potential energy when the body is at a height of 20 m.

### Step 3: Calculate the potential energy after falling 5 m (at 15 m)
After falling 5 m, the height of the body is now 15 m. The potential energy (PE_after_fall) at this height can be calculated as:
\[ PE_{\text{after fall}} = mg \times 15 \]

### Step 4: Determine the change in potential energy
To find out how much potential energy has been lost after falling 5 m, we can calculate the difference between the initial potential energy and the potential energy after falling:
\[ \Delta PE = PE_{\text{initial}} - PE_{\text{after fall}} \]
Substituting the values:
\[ \Delta PE = mg \times 20 - mg \times 15 \]
\[ \Delta PE = mg(20 - 15) = mg \times 5 \]

### Step 5: Calculate the fraction of potential energy lost
Now, we can find the fraction of potential energy lost compared to the initial potential energy:
\[ \text{Fraction lost} = \frac{\Delta PE}{PE_{\text{initial}}} = \frac{mg \times 5}{mg \times 20} = \frac{5}{20} = \frac{1}{4} \]

### Conclusion
After falling through a distance of 5 m, the body loses \( \frac{1}{4} \) of its total potential energy.