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`

Explanation

To find the height at which the object is located with respect to the ground, we can use the formula for gravitational potential energy:

\[ PE = mgh \]

Where:
- \( PE \) is the potential energy,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height above the ground.

### Step-by-Step Solution:

1. **Identify the known 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:**
\[ PE = mgh \]

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

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

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

6. **Now substitute this value back into the equation for height:**
\[ h = \frac{480 \, \text{J}}{120 \, \text{kg m/s}^2} \]

7. **Perform the division:**
\[ h = 4 \, \text{m} \]

### Conclusion:
The height at which the object is located with respect to the ground is **4 meters**.