A body possess potential energy of 460 J whose mass is 20 kg and is raised to a certain height. What is the height when `g = 10 m//s ^(2) ` ?

Options

A. 1.7 m
B. 2.3 m
C. 3.9 m
D. 4.1 m

Explanation

To find the height at which the body possesses a potential energy of 460 J, we can use the formula for gravitational potential energy (PE):

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

Where:
- \( PE \) = potential energy (in joules)
- \( m \) = mass of the body (in kg)
- \( g \) = acceleration due to gravity (in m/s²)
- \( h \) = height (in meters)

### Step 1: Write down the given values
- Potential Energy (PE) = 460 J
- Mass (m) = 20 kg
- Acceleration due to gravity (g) = 10 m/s²

### Step 2: Substitute the values into the formula
Using the formula for potential energy:

\[ 460 = 20 \cdot 10 \cdot h \]

### Step 3: Simplify the equation
First, calculate \( 20 \cdot 10 \):

\[ 20 \cdot 10 = 200 \]

Now, the equation becomes:

\[ 460 = 200 \cdot h \]

### Step 4: Solve for height (h)
To find \( h \), we can rearrange the equation:

\[ h = \frac{460}{200} \]

### Step 5: Calculate the value of h
Now, perform the division:

\[ h = \frac{460}{200} = 2.3 \, \text{m} \]

### Final Answer
The height \( h \) at which the body possesses a potential energy of 460 J is **2.3 meters**.

---