A freely falling body takes `4s` to reach the ground. One second after release, the percentage of its potential energy, that is still retained is

Options

A. `6.25 %`
B. `25 %`
C. `37.5 %`
D. `93.75 %`

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Problem**:
A freely falling body takes 4 seconds to reach the ground. We need to find the percentage of potential energy retained after 1 second of free fall.

2. **Finding the Height (H)**:
We can use the second equation of motion to find the height from which the body falls. The equation is:
\[ S = ut + \frac{1}{2}gt^2 \]
Here, \( S \) is the displacement (which will be equal to the height \( H \)), \( u \) is the initial velocity (0 for a freely falling body), \( g \) is the acceleration due to gravity, and \( t \) is the time taken (4 seconds).
\[ H = 0 \cdot 4 + \frac{1}{2}g(4^2) = \frac{1}{2}g(16) = 8g \]

3. **Finding the Height after 1 Second (H1)**:
Now, we need to find the height fallen after 1 second. We use the same equation:
\[ H_1 = 0 \cdot 1 + \frac{1}{2}g(1^2) = \frac{1}{2}g(1) = \frac{g}{2} \]

4. **Finding the Remaining Height (H2)**:
The height above the ground after 1 second is:
\[ H_2 = H - H_1 = 8g - \frac{g}{2} = 8g - 0.5g = \frac{15g}{2} \]

5. **Calculating the Potential Energy**:
The potential energy at a height \( H \) is given by:
\[ PE = mgh \]
Therefore, the potential energy at height \( H \) is:
\[ PE_H = mg(8g) = 8mg \]
The potential energy at height \( H_2 \) is:
\[ PE_{H2} = mg\left(\frac{15g}{2}\right) = \frac{15mg}{2} \]

6. **Finding the Percentage of Potential Energy Retained**:
The percentage of potential energy retained after 1 second is given by:
\[ \text{Percentage} = \left(\frac{PE_{H2}}{PE_H}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage} = \left(\frac{\frac{15mg}{2}}{8mg}\right) \times 100 = \left(\frac{15}{16}\right) \times 100 = 93.75\% \]

### Final Answer:
The percentage of potential energy that is still retained after 1 second is **93.75%**.