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. `4J//kg`
B. `7J//kg`
C. `-3J//kg`
D. `-7J//kg`

Answer

To solve the problem, we need to find the potential difference between points B and A given the following information:

- Mass (m) = 2 kg
- Increase in kinetic energy (ΔKE) = 4 J
- Work done by the person (W) = -10 J

### Step-by-Step Solution:

1. **Understanding the Work-Energy Principle**:
The work done on the mass is equal to the change in mechanical energy, which includes both potential energy and kinetic energy. Mathematically, this can be expressed as:
\[ W = \Delta PE + \Delta KE \]
where:
- \( \Delta PE = PE_B - PE_A \) (change in potential energy)
- \( \Delta KE = KE_B - KE_A \) (change in kinetic energy)

2. **Substituting Known Values**:
We know:
- \( W = -10 \, \text{J} \)
- \( \Delta KE = 4 \, \text{J} \)

Plugging these values into the equation gives:
\[ -10 = (PE_B - PE_A) + 4 \]

3. **Rearranging the Equation**:
To isolate the change in potential energy, we rearrange the equation:
\[ PE_B - PE_A = -10 - 4 \]
\[ PE_B - PE_A = -14 \, \text{J} \]

4. **Relating Potential Energy to Potential**:
The potential energy (PE) can be expressed in terms of potential (V) and mass (m):
\[ PE = m \cdot V \]
Therefore, we can write:
\[ PE_B - PE_A = m(V_B - V_A) \]
Substituting the mass (m = 2 kg) into the equation:
\[ -14 = 2(V_B - V_A) \]

5. **Solving for the Potential Difference**:
Dividing both sides by 2 gives:
\[ V_B - V_A = \frac{-14}{2} = -7 \, \text{J/kg} \]

6. **Conclusion**:
The potential difference between points B and A is:
\[ V_B - V_A = -7 \, \text{J/kg} \]

### Final Answer:
The potential difference between B and A is **-7 J/kg**.