An object of mass 12 kg is at a certain height above the gorund if the potential energy of the object is 480J find the height at which the object is withj respect to the ground Given, ` g = 10m//s^2`

Options

A. `2m`
B. `3m`
C. `4m`
D. `5m`

Explanation

To find the height at which the object is located above the ground based on its potential energy, we can use the formula for potential energy (PE):

\[ PE = m \cdot g \cdot h \]

Where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (in meters per second squared),
- \( h \) is the height above the ground (in meters).

### Step-by-step Solution:

1. **Identify the given values:**
- Mass of the object, \( m = 12 \, \text{kg} \)
- Potential energy, \( PE = 480 \, \text{J} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Write the formula for potential energy:**
\[ PE = m \cdot g \cdot h \]

3. **Rearrange the formula to solve for height \( h \):**
\[ h = \frac{PE}{m \cdot g} \]

4. **Substitute the known values into the equation:**
\[ h = \frac{480 \, \text{J}}{12 \, \text{kg} \cdot 10 \, \text{m/s}^2} \]

5. **Calculate the denominator:**
\[ m \cdot g = 12 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 120 \, \text{kg m/s}^2 \]

6. **Now divide the potential energy by the result from step 5:**
\[ h = \frac{480 \, \text{J}}{120 \, \text{kg m/s}^2} = 4 \, \text{m} \]

7. **Conclusion:**
The height \( h \) at which the object is located above the ground is:
\[ h = 4 \, \text{m} \]

### Final Answer:
The object is at a height of **4 meters** above the ground.