If two persons A and B take 2 seconds and 4 seconds respectively to lift an object to the same height h, then the ratio of their potential energies at highest point is

Options

A. `1:2`
B. `1:1`
C. `2:1`
D. `1:3`

Answer

To solve the problem, we need to determine the potential energies of two persons, A and B, who lift an object to the same height \( h \) in different times.

### Step-by-Step Solution:

1. **Understanding Potential Energy**:
The potential energy (PE) of an object at a height \( h \) is given by the formula:
\[ PE = mgh \]
where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height.

2. **Identifying the Variables**:
- Let \( m \) be the mass of the object.
- Let \( g \) be the acceleration due to gravity (which is constant).
- Both A and B lift the object to the same height \( h \).

3. **Calculating Potential Energy for A**:
Since person A lifts the object to height \( h \), the potential energy of the object when lifted by A is:
\[ PE_A = mgh \]

4. **Calculating Potential Energy for B**:
Similarly, for person B, who also lifts the object to height \( h \), the potential energy is:
\[ PE_B = mgh \]

5. **Finding the Ratio of Potential Energies**:
To find the ratio of their potential energies, we calculate:
\[ \text{Ratio} = \frac{PE_A}{PE_B} = \frac{mgh}{mgh} = 1 \]

6. **Conclusion**:
The ratio of the potential energies at the highest point for both persons A and B is:
\[ \frac{PE_A}{PE_B} = 1:1 \]

### Final Answer:
The ratio of their potential energies at the highest point is \( 1:1 \).

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