A person brings a mass of `1 kg` from infinity to a point `A`. Initially the mass was at rest but it moves with a speed of `2 m//s` as it reaches `A`. The work done by the person on a mass is `-3 J`. The potential of `A` is:

Options

A. -2 J/Kg
B. -4 J/kg
C. -5 J/kg
D. None of the above

Answer

To find the potential at point A, we can follow these steps:

### Step 1: Calculate the Kinetic Energy (KE) at Point A
The kinetic energy of an object can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass (1 kg)
- \( v \) is the speed (2 m/s)

Substituting the values:
\[ KE = \frac{1}{2} \times 1 \, \text{kg} \times (2 \, \text{m/s})^2 = \frac{1}{2} \times 1 \times 4 = 2 \, \text{J} \]

### Step 2: Use the Work-Energy Principle
According to the work-energy principle, the work done on the mass is equal to the change in kinetic energy plus the change in potential energy. In this case, since the mass is brought from infinity to point A, we can express this as:
\[ W = PE + KE \]
Where:
- \( W \) is the work done (−3 J)
- \( PE \) is the potential energy at point A
- \( KE \) is the kinetic energy at point A (2 J)

### Step 3: Rearranging the Equation to Find Potential Energy
Rearranging the equation gives us:
\[ PE = W - KE \]
Substituting the known values:
\[ PE = -3 \, \text{J} - 2 \, \text{J} = -5 \, \text{J} \]

### Step 4: Calculate the Potential per Unit Mass
The potential per unit mass (gravitational potential) at point A can be calculated using the formula:
\[ \text{Potential} = \frac{PE}{m} \]
Substituting the values:
\[ \text{Potential} = \frac{-5 \, \text{J}}{1 \, \text{kg}} = -5 \, \text{J/kg} \]

### Final Answer
The potential at point A is:
\[ \text{Potential} = -5 \, \text{J/kg} \]

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