The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point `P` be `-5 J kg^(-1)`. Suppose, we arbitrarily assume the gravitational potential at infinity to be `+10 J kg^(-1)`, then the gravitational potential at `P` will be

Options

A. `-5Jkg^(-1)`
B. `+5Jkg^(-1)`
C. `-15Jkg^(-1)`
D. `+15Jkg^(-1)`

Explanation

To solve the problem, we need to understand how gravitational potential is defined and how it can change based on our reference point.

### Step-by-Step Solution:

1. **Understanding Gravitational Potential**:
The gravitational potential \( V \) at a point in a gravitational field is defined as the work done per unit mass to bring a mass from infinity to that point. The potential at infinity is typically taken to be zero.

2. **Given Information**:
- The gravitational potential at point \( P \) is given as \( V_P = -5 \, \text{J kg}^{-1} \).
- We are considering a new arbitrary reference point where the gravitational potential at infinity is assumed to be \( V_{\infty} = +10 \, \text{J kg}^{-1} \).

3. **Potential Difference Concept**:
The gravitational potential difference between two points is what matters in this context. The potential difference between point \( P \) and infinity is given by:
\[ \Delta V = V_P - V_{\infty} \]

4. **Calculating the Potential Difference**:
Substituting the values we have:
\[ \Delta V = V_P - V_{\infty} = -5 - 10 = -15 \, \text{J kg}^{-1} \]

5. **Finding the New Potential at Point \( P \)**:
To maintain the same potential difference when we change the reference potential at infinity, we can set up the equation:
\[ V_{P'} - V_{\infty}' = -5 \]
where \( V_{\infty}' \) is the new potential at infinity (which is \( +10 \, \text{J kg}^{-1} \)).

Rearranging gives:
\[ V_{P'} = -5 + V_{\infty}' = -5 + 10 = +5 \, \text{J kg}^{-1} \]

6. **Conclusion**:
Therefore, the gravitational potential at point \( P \) when the potential at infinity is assumed to be \( +10 \, \text{J kg}^{-1} \) is:
\[ V_{P'} = +5 \, \text{J kg}^{-1} \]

### Final Answer:
The gravitational potential at point \( P \) is \( +5 \, \text{J kg}^{-1} \).

---