A stone of mass 1 kg falls to the earth from a height of 10 m. The kinetic energy of the stone when it is 4 m above the ground is

Options

A. 58.8 J
B. 5.88 J
C. 588 J
D. none of these

Answer

To find the kinetic energy of a stone of mass 1 kg when it is 4 m above the ground after falling from a height of 10 m, we can use the principle of conservation of mechanical energy. Here’s the step-by-step solution:

### Step 1: Identify the initial and final heights
- The initial height (H1) from which the stone falls is 10 m.
- The final height (H2) when we want to find the kinetic energy is 4 m.

### Step 2: Calculate the potential energy at the initial height
The potential energy (PE) at height H1 can be calculated using the formula:
\[ PE = mgh \]
Where:
- \( m = 1 \, \text{kg} \) (mass of the stone)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = H1 = 10 \, \text{m} \)

Calculating the potential energy:
\[ PE_{initial} = 1 \times 9.8 \times 10 = 98 \, \text{J} \]

### Step 3: Calculate the potential energy at the final height
Now, we calculate the potential energy at height H2 (4 m):
\[ PE_{final} = mgh \]
Where:
- \( h = H2 = 4 \, \text{m} \)

Calculating the potential energy:
\[ PE_{final} = 1 \times 9.8 \times 4 = 39.2 \, \text{J} \]

### Step 4: Apply the conservation of mechanical energy
According to the conservation of mechanical energy:
\[ PE_{initial} + KE_{initial} = PE_{final} + KE_{final} \]
Since the stone is initially at rest, the initial kinetic energy (KE_initial) is 0:
\[ 98 \, \text{J} + 0 = 39.2 \, \text{J} + KE_{final} \]

### Step 5: Solve for the final kinetic energy
Rearranging the equation to find \( KE_{final} \):
\[ KE_{final} = PE_{initial} - PE_{final} \]
Substituting the values:
\[ KE_{final} = 98 \, \text{J} - 39.2 \, \text{J} = 58.8 \, \text{J} \]

### Final Answer
The kinetic energy of the stone when it is 4 m above the ground is **58.8 Joules**.

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