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 ratio of potential energies of two persons A and B lifting an object to the same height h.

### Step-by-Step Solution:

1. **Understand the Concept of Potential Energy**:
- The potential energy (PE) of an object at a height h is given by the formula:
\[ PE = mgh \]
where:
- \( m \) = mass of the object,
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) = height to which the object is lifted.

2. **Identify the Given Information**:
- Person A takes 2 seconds to lift the object to height \( h \).
- Person B takes 4 seconds to lift the same object to the same height \( h \).

3. **Calculate Potential Energies**:
- For both persons A and B, since they lift the object to the same height \( h \), the potential energy for both will be the same.
- Therefore, the potential energy for person A is:
\[ PE_A = mgh \]
- Similarly, the potential energy for person B is:
\[ PE_B = mgh \]

4. **Find the Ratio of Potential Energies**:
- The ratio of the potential energies of A and B is given by:
\[ \text{Ratio} = \frac{PE_A}{PE_B} = \frac{mgh}{mgh} \]
- Simplifying this gives:
\[ \text{Ratio} = 1 \]

5. **Conclusion**:
- The ratio of their potential energies at the highest point is:
\[ \text{Ratio} = 1:1 \]

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

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