चन्द्रमा पर गुरुत्वाकर्षण के कारण त्वरण है ?

Options

A. पृथ्वी का `((1)/(6))^(th)`
B. पृथ्वी के सामान
C. पृथ्वी का `((1)/(3))^(rd)`
D. पृथ्वी का `((1)/(5))^(th)`

Explanation

### Step-by-Step Solution:

1. **Understanding the Question**: We need to find the acceleration due to gravity on the Moon. The question specifically asks for the value of gravitational acceleration on the Moon.

2. **Gravitational Acceleration on Earth**: We know that the gravitational acceleration on Earth (G) is approximately 9.81 m/s².

3. **Gravitational Acceleration on the Moon**: The gravitational acceleration on the Moon (G') is known to be approximately 1.62 m/s².

4. **Comparing the Two Values**: To understand how the Moon's gravitational acceleration compares to that of Earth, we can express it as a fraction of Earth's gravitational acceleration:
\[ \text{Comparison} = \frac{G'}{G} = \frac{1.62 \, \text{m/s}^2}{9.81 \, \text{m/s}^2} \]

5. **Calculating the Ratio**: Performing the division:
\[ \frac{1.62}{9.81} \approx 0.165 \]
This means that the gravitational acceleration on the Moon is approximately 0.165 times that of Earth.

6. **Expressing as a Fraction**: This can also be expressed as:
\[ G' \approx \frac{1}{6} G \]
Thus, the gravitational acceleration on the Moon is about 1/6th that of Earth.

7. **Final Answer**: Therefore, the acceleration due to gravity on the Moon is approximately 1.62 m/s².