If a person jumps 1 m at the surface of the earth , he will jump 6 meteres at the surface of the moon .l heretore , the ratio of moon 's acceleration due to gravity with respect to earth 's acceleration due to gravity would be

Options

A. 6
B. `1//6`
C. `0.6`
D. `0.06`

Answer

To solve the problem, we need to find the ratio of the moon's acceleration due to gravity (g_m) to the Earth's acceleration due to gravity (g_e) based on the heights a person can jump on each celestial body.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- A person jumps 1 meter on Earth (h_e = 1 m).
- The same person jumps 6 meters on the Moon (h_m = 6 m).

2. **Use the Equation of Motion**:
- We can use the equation of motion that relates the height of the jump to the acceleration due to gravity:
\[ h = \frac{u^2}{2g} \]
- Here, \( h \) is the height of the jump, \( u \) is the initial velocity (which we can assume is the same for both jumps), and \( g \) is the acceleration due to gravity.

3. **Set Up the Ratios**:
- Rearranging the equation gives us:
\[ g = \frac{u^2}{2h} \]
- Therefore, the acceleration due to gravity can be expressed as inversely proportional to the height of the jump:
\[ g \propto \frac{1}{h} \]

4. **Relate the Accelerations**:
- From the above relationship, we can write:
\[ \frac{g_m}{g_e} = \frac{h_e}{h_m} \]

5. **Substitute the Values**:
- Substitute the heights into the equation:
\[ \frac{g_m}{g_e} = \frac{1 \, \text{m}}{6 \, \text{m}} = \frac{1}{6} \]

6. **Conclusion**:
- The ratio of the moon's acceleration due to gravity to the Earth's acceleration due to gravity is:
\[ \frac{g_m}{g_e} = \frac{1}{6} \]

### Final Answer:
The ratio of the moon's acceleration due to gravity with respect to Earth's acceleration due to gravity is \( \frac{1}{6} \).

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