A capillary tube is taken from the Earth to the surface of the moon. The rise of the liquid column on the Moon (acceleration due to gravity on the Earth is 6 times that of the Moon) is

Options

A. six times that on the earth's surface
B. 1/6 that on tha earth surface
C. equal on that of the earth surface
D. zero

Explanation

To solve the problem of the rise of a liquid column in a capillary tube on the Moon, we can follow these steps:

### Step 1: Understand the formula for capillary rise
The height \( h \) of the liquid column in a capillary tube is given by the formula:
\[ h = \frac{2 \gamma \cos \theta}{r \rho g} \]
where:
- \( \gamma \) is the surface tension of the liquid,
- \( \theta \) is the contact angle,
- \( r \) is the radius of the capillary tube,
- \( \rho \) is the density of the liquid,
- \( g \) is the acceleration due to gravity.

### Step 2: Analyze the relationship between height and gravity
From the formula, we can see that the height \( h \) is inversely proportional to the acceleration due to gravity \( g \). This means that as \( g \) increases, \( h \) decreases, and vice versa.

### Step 3: Set up the ratio of heights on Earth and Moon
Let \( h_{Earth} \) be the height of the liquid column on Earth and \( h_{Moon} \) be the height of the liquid column on the Moon. We can write the relationship as:
\[ \frac{h_{Moon}}{h_{Earth}} = \frac{g_{Earth}}{g_{Moon}} \]

### Step 4: Substitute the relationship between gravitational accelerations
It is given that the acceleration due to gravity on Earth is 6 times that of the Moon:
\[ g_{Earth} = 6 \cdot g_{Moon} \]
Substituting this into the ratio gives:
\[ \frac{h_{Moon}}{h_{Earth}} = \frac{6 \cdot g_{Moon}}{g_{Moon}} = 6 \]

### Step 5: Conclude the relationship
From the above equation, we can conclude that:
\[ h_{Moon} = 6 \cdot h_{Earth} \]
This means that the rise of the liquid column on the Moon is 6 times that of the rise on Earth.

### Final Answer
The rise of the liquid column on the Moon is 6 times the rise of the liquid column on Earth.

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