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 calculate the work done in moving a mass of 2 kg from the surface of the 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. **Understand the Given Information:**
- Gravitational potential difference (ΔV) between the surface and a point 10 m above is 4 J/kg.
- Mass (m) to be moved is 2 kg.
- Height (h') to which the mass is moved is 5 m.

2. **Calculate the Gravitational Field (g):**
- The gravitational potential difference is given by:
\[ \Delta V = g \cdot h \]
- We know that for a height of 10 m, ΔV = 4 J/kg. Therefore:
\[ 4 = g \cdot 10 \]
- Rearranging gives:
\[ g = \frac{4}{10} = 0.4 \text{ m/s}^2 \]

3. **Calculate the Work Done (W):**
- The work done in moving the mass is given by the change in gravitational potential energy (U):
\[ W = m \cdot g \cdot h' \]
- Here, h' = 5 m. Substituting the values:
\[ W = 2 \cdot 0.4 \cdot 5 \]
- Calculating this gives:
\[ W = 2 \cdot 0.4 \cdot 5 = 4 \text{ J} \]

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 J**.