Gravitational potential difference between a point on surface of planet and another point 10 m above is 4J/kg. Considering gravitational field to be uniform, how much work is donw in moving a mass of 2kg from the surface to a point 5 m above the surface?

Options

A. 4J
B. 5J
C. 6J
D. 7J

Explanation

To solve the problem, we need to find the work done in moving a mass of 2 kg from the surface of a planet to a point 5 m above the surface, given that the gravitational potential difference between the surface and a point 10 m above is 4 J/kg.

### Step-by-Step Solution:

1. **Identify the Gravitational Potential Difference**:
The gravitational potential difference (ΔV) between the surface of the planet and a point 10 m above is given as 4 J/kg.

2. **Calculate the Gravitational Field Intensity (g)**:
The gravitational potential difference is related to the gravitational field intensity (g) and the height difference (Δh). The formula is:
\[ \Delta V = g \cdot \Delta h \]
Here, Δh = 10 m. Rearranging the formula gives:
\[ g = \frac{\Delta V}{\Delta h} = \frac{4 \, \text{J/kg}}{10 \, \text{m}} = 0.4 \, \text{J/(kg·m)} \]

3. **Calculate the Work Done (W)**:
The work done in moving a mass (m) in a gravitational field over a height (h) is given by:
\[ W = m \cdot g \cdot h \]
Here, m = 2 kg and h = 5 m. Substituting the values:
\[ W = 2 \, \text{kg} \cdot 0.4 \, \text{J/(kg·m)} \cdot 5 \, \text{m} = 4 \, \text{J} \]

4. **Final Answer**:
The work done in moving the mass of 2 kg from the surface to a point 5 m above the surface is **4 Joules**.