A man can jump 2 m high on the surface of the earth. How high he can jump on a planet where the acceleration due to gravity is `(g)/(12)`, where g is the acceleration due to gravity on the surface of the earth ?

Options

A. 12 m
B. 18 m
C. 24 m
D. 30 m

Explanation

To solve the problem, we need to understand how the height a person can jump is related to the acceleration due to gravity. The height a person can jump is inversely proportional to the acceleration due to gravity. This means that if gravity decreases, the height a person can jump increases.

### Step-by-Step Solution:

1. **Identify the known values**:
- The height a man can jump on Earth, \( h_{E} = 2 \, \text{m} \).
- The acceleration due to gravity on Earth, \( g \).
- The acceleration due to gravity on the other planet, \( g' = \frac{g}{12} \).

2. **Understand the relationship**:
The height a person can jump is inversely proportional to the acceleration due to gravity. This can be expressed mathematically as:
\[ h \propto \frac{1}{g} \]
Therefore, we can set up a ratio:
\[ \frac{h_{E}}{h_{P}} = \frac{g'}{g} \]
where \( h_{P} \) is the height the man can jump on the planet.

3. **Substituting the known values**:
Substitute \( h_{E} = 2 \, \text{m} \) and \( g' = \frac{g}{12} \):
\[ \frac{2}{h_{P}} = \frac{\frac{g}{12}}{g} \]

4. **Simplifying the equation**:
The \( g \) terms cancel out:
\[ \frac{2}{h_{P}} = \frac{1}{12} \]

5. **Cross-multiplying to solve for \( h_{P} \)**:
\[ 2 \cdot 12 = h_{P} \]
\[ h_{P} = 24 \, \text{m} \]

6. **Conclusion**:
The man can jump 24 meters high on the planet where the acceleration due to gravity is \( \frac{g}{12} \).

### Final Answer:
The height the man can jump on the planet is **24 meters**.