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, we need to find the work done in taking a 5 kg body to a height of 4 meters above the surface of a planet, given that the gravitational potential difference between the surface and a point 20 meters above is 2 joules/kg.

### Step-by-Step Solution:

1. **Identify the Gravitational Potential Difference:**
The gravitational potential difference (ΔVg) between the surface of the planet and a point 20 meters above is given as:
\[ \Delta V_g = 2 \, \text{J/kg} \]

2. **Calculate the Gravitational Field (Eg):**
The gravitational potential difference is related to the gravitational field (Eg) by the formula:
\[ \Delta V_g = -E_g \cdot d \]
where \(d\) is the height difference (20 m in this case). Rearranging the formula gives:
\[ E_g = -\frac{\Delta V_g}{d} \]
Plugging in the values:
\[ E_g = -\frac{2 \, \text{J/kg}}{20 \, \text{m}} = -0.1 \, \text{J/(kg·m)} = -\frac{1}{10} \, \text{J/(kg·m)} \]

3. **Determine the Work Done (W):**
The work done in moving a mass \(m\) through a height \(h\) in a gravitational field is given by:
\[ W = m \cdot \Delta V_g \]
First, we need to find the gravitational potential difference for moving the 5 kg body to a height of 4 meters. The potential difference for this height can be calculated using:
\[ \Delta V_g = -E_g \cdot h \]
where \(h = 4 \, \text{m}\). Substituting the values:
\[ \Delta V_g = -\left(-\frac{1}{10}\right) \cdot 4 = \frac{4}{10} = 0.4 \, \text{J/kg} \]

4. **Calculate the Total Work Done:**
Now, substituting \(m = 5 \, \text{kg}\) and \(\Delta V_g = 0.4 \, \text{J/kg}\):
\[ W = 5 \, \text{kg} \cdot 0.4 \, \text{J/kg} = 2 \, \text{J} \]

### Final Answer:
The work done in taking the 5 kg body to a height of 4 meters above the surface of the planet is:
\[ \boxed{2 \, \text{J}} \]