A person brings a mass `2kg` from `A` to `B`. The increase in kinetic energy of mass is `4J` and work done by the person on the mass is `-10J`. The potential difference between `B` and `A` is ......`J//kg`

Options

A. `4`
B. `7`
C. `-3`
D. `-7`

Explanation

To solve the problem, we will use the principle of conservation of energy. The work-energy principle states that the total mechanical energy of an object is conserved if only conservative forces are acting on it.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass (m) = 2 kg
- Increase in kinetic energy (ΔKE) = 4 J
- Work done by the person (W) = -10 J

2. **Apply the Work-Energy Principle:**
The change in mechanical energy can be expressed as:
\[ \Delta KE + W = \Delta PE \]
where \(\Delta PE\) is the change in potential energy.

3. **Substitute the Known Values:**
\[ 4 J - 10 J = \Delta PE \]
\[ \Delta PE = -6 J \]

4. **Relate Change in Potential Energy to Potential Difference:**
The change in potential energy is related to the potential difference (V) between points A and B by the formula:
\[ \Delta PE = m \cdot g \cdot (V_B - V_A) \]
where \(g\) is the acceleration due to gravity (approximately \(9.81 \, m/s^2\)).

5. **Calculate Potential Difference:**
Rearranging the equation gives:
\[ V_B - V_A = \frac{\Delta PE}{m \cdot g} \]
Substituting the values:
\[ V_B - V_A = \frac{-6 J}{2 kg \cdot 9.81 m/s^2} \]
\[ V_B - V_A = \frac{-6}{19.62} \approx -0.306 J/kg \]

6. **Final Result:**
The potential difference between B and A is approximately:
\[ V_B - V_A \approx -0.306 \, J/kg \]