An object of mass 1 kg has a P.E. of 1 J relative to the ground when it is at a height of about

Options

A. 0.102 m
B. 1 m
C. 9.8 m
D. 32 m

Explanation

To find the height at which an object of mass 1 kg has a potential energy of 1 Joule relative to the ground, we can use the formula for gravitational potential energy (P.E.):

### Step-by-Step Solution:

1. **Understand the Formula for Potential Energy**:
The potential energy (P.E.) of an object at height \( h \) is given by the formula:
\[ P.E. = mgh \]
where:
- \( m \) = mass of the object (in kg)
- \( g \) = acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \))
- \( h \) = height above the ground (in meters)

2. **Set Up the Equation**:
According to the problem, the potential energy is given as 1 Joule. Therefore, we can set up the equation:
\[ 1 = mgh \]

3. **Substitute the Known Values**:
We know the mass \( m = 1 \, \text{kg} \) and \( g = 9.8 \, \text{m/s}^2 \). Substituting these values into the equation gives:
\[ 1 = 1 \cdot 9.8 \cdot h \]

4. **Solve for Height \( h \)**:
Rearranging the equation to solve for \( h \):
\[ h = \frac{1}{1 \cdot 9.8} = \frac{1}{9.8} \]
Calculating this gives:
\[ h \approx 0.102 \, \text{m} \]

5. **Conclusion**:
The height at which the object has a potential energy of 1 Joule is approximately \( 0.102 \, \text{m} \).

### Final Answer:
The height is approximately **0.102 m**.

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