An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given. `g=10 ms^(-2)`.

Options

A. 5m
B. 8m
C. 4m
D. 6m

Answer

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

\[ PE = mgh \]

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 given values:**
- Mass (\( m \)) = 12 kg
- Potential Energy (\( PE \)) = 480 J
- Gravitational acceleration (\( g \)) = 10 m/s²

2. **Substitute the known values into the potential energy formula:**
\[ 480 = 12 \times 10 \times h \]

3. **Simplify the equation:**
\[ 480 = 120h \]

4. **Solve for height (\( h \)):**
\[ h = \frac{480}{120} \]

5. **Calculate the height:**
\[ h = 4 \text{ meters} \]

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