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

Options

A. 0.0625
B. 0.25
C. 0.375
D. 0.9375

Answer

To solve the problem step by step, we will first calculate the initial potential energy of the body when it is released and then determine how much potential energy remains after one second of free fall.

### Step 1: Calculate the total distance fallen in 4 seconds
The formula for the distance \( s \) fallen under gravity is given by:
\[ s = \frac{1}{2} g t^2 \]
where \( g \) is the acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \)) and \( t \) is the time in seconds.

For a freely falling body that takes 4 seconds to reach the ground:
\[ s_1 = \frac{1}{2} \times 10 \times (4^2) = \frac{1}{2} \times 10 \times 16 = 80 \, \text{meters} \]

### Step 2: Calculate the distance fallen after 1 second
Now, we calculate the distance fallen after 1 second:
\[ s_2 = \frac{1}{2} \times 10 \times (1^2) = \frac{1}{2} \times 10 \times 1 = 5 \, \text{meters} \]

### Step 3: Calculate the initial potential energy
The initial potential energy \( U_1 \) when the body is at height \( s_1 \) is given by:
\[ U_1 = m \cdot g \cdot s_1 = m \cdot 10 \cdot 80 = 800m \, \text{Joules} \]

### Step 4: Calculate the potential energy after 1 second
The potential energy \( U_2 \) after falling for 1 second to height \( s_2 \) is:
\[ U_2 = m \cdot g \cdot s_2 = m \cdot 10 \cdot 75 = 750m \, \text{Joules} \]
(Note: The height after 1 second is \( 80 - 5 = 75 \) meters.)

### Step 5: Calculate the percentage of potential energy retained
To find the percentage of initial potential energy that is still retained after 1 second, we use the formula:
\[ \text{Percentage retained} = \frac{U_2}{U_1} \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage retained} = \frac{750m}{800m} \times 100 = \frac{750}{800} \times 100 = 93.75\% \]

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

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