The acceleration due to gravity on the planet `A` is `9` times the acceleration due to gravity on planet `B`. A man jumps to a height of `2m` on the surface of `A`. What is the height of jump by the same person on the planet `B`?

Options

A. `6m`
B. `(2)/(3)m`
C. `(2)/(9)m`
D. `18m`

Answer

To solve the problem, we need to relate the heights a man can jump on two different planets (A and B) based on their respective gravitational accelerations.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Let \( g_A \) be the acceleration due to gravity on planet A.
- Let \( g_B \) be the acceleration due to gravity on planet B.
- We are given that \( g_A = 9 g_B \).
- The height jumped on planet A, \( H_A = 2 \, \text{m} \).

2. **Understanding the Relationship Between Height and Gravity:**
- The height a person can jump is inversely proportional to the acceleration due to gravity. This means:
\[ H \propto \frac{1}{g} \]
- Thus, we can write:
\[ \frac{g_A}{g_B} = \frac{H_B}{H_A} \]
- Where \( H_B \) is the height jumped on planet B.

3. **Substituting the Known Values:**
- From the relationship we established, substituting \( g_A = 9 g_B \) and \( H_A = 2 \, \text{m} \):
\[ \frac{9 g_B}{g_B} = \frac{H_B}{2} \]

4. **Simplifying the Equation:**
- The \( g_B \) terms cancel out:
\[ 9 = \frac{H_B}{2} \]

5. **Solving for \( H_B \):**
- Multiply both sides by 2 to find \( H_B \):
\[ H_B = 9 \times 2 = 18 \, \text{m} \]

6. **Conclusion:**
- The height of the jump by the same person on planet B is \( H_B = 18 \, \text{m} \).

### Final Answer:
The height of jump by the same person on planet B is **18 meters**.

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