Gravitational potential difference between surface of a planet and a point situated at a height of 20 m above its surface is 2joule/kg. if gravitational field is uniform, then the work done in taking a 5kg body of height 4 meter above surface will be-:

Options

A. 2J
B. 20 J
C. 40 J
D. 10 J

Explanation

To solve the problem step by step, we will follow the logic presented in the video transcript and break it down into clear steps.

### Step 1: Understand the Given Information
We are given:
- Gravitational potential difference (ΔV) between the surface of a planet and a point at a height of 20 m is 2 J/kg.
- We need to find the work done in lifting a 5 kg body to a height of 4 m above the surface.

### Step 2: Relate Gravitational Potential Difference to Gravitational Field
The gravitational potential difference (ΔV) can be expressed in terms of the gravitational field (E) and the height (h):
\[ \Delta V = -E \cdot h \]
Given that ΔV = 2 J/kg and h = 20 m:
\[ 2 = -E \cdot 20 \]

### Step 3: Solve for the Gravitational Field (E)
Rearranging the equation to find E:
\[ E = -\frac{2}{20} = -0.1 \text{ J/kg} \]
Since we are interested in the magnitude of the gravitational field, we take:
\[ E = 0.1 \text{ J/kg} \]

### Step 4: Calculate the Work Done in Lifting the Body
The work done (W) in lifting a mass (m) to a height (h) in a uniform gravitational field can be calculated using the formula:
\[ W = m \cdot \Delta V \]
Where ΔV is the change in gravitational potential energy, which can be calculated as:
\[ \Delta V = E \cdot h \]
For our case, we need to find the change in potential energy when lifting the body to a height of 4 m:
\[ \Delta V = 0.1 \cdot 4 = 0.4 \text{ J/kg} \]

### Step 5: Substitute Values to Find Work Done
Now we can calculate the work done:
\[ W = 5 \text{ kg} \cdot 0.4 \text{ J/kg} = 2 \text{ J} \]

### Conclusion
The work done in taking a 5 kg body to a height of 4 m above the surface is **2 Joules**.