The height of liquid column in the capillary on the surface of Moon ,if it is h on surface of the Earth is

Options

A. h
B. `h/6`
C. 6h
D. zero

Answer

To solve the problem of determining the height of the liquid column in a capillary tube on the surface of the Moon, given that the height on the surface of the Earth is \( h \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Identify Constants**:
When moving from Earth to the Moon, the following parameters remain constant:
- Surface tension \( T \) does not change as it is an intrinsic property of the liquid.
- The angle of contact \( \theta \) remains the same as it depends on the interaction between the liquid and the tube.
- The radius \( r \) of the capillary tube is constant.
- The density \( \rho \) of the liquid remains constant as the mass and volume do not change.

3. **Consider the Change in Gravity**:
The only variable that changes when moving from Earth to the Moon is the acceleration due to gravity \( g \). The acceleration due to gravity on the Moon (\( g_{moon} \)) is approximately \( \frac{1}{6} \) of that on Earth (\( g_{earth} \)):
\[ g_{moon} = \frac{g_{earth}}{6} \]

4. **Set Up the Proportionality**:
Since the height of the liquid column is inversely proportional to gravity, we can set up the following relationship:
\[ \frac{h_{moon}}{h_{earth}} = \frac{g_{earth}}{g_{moon}} \]

5. **Substitute the Values**:
Substitute \( g_{moon} \) into the equation:
\[ \frac{h_{moon}}{h} = \frac{g}{\frac{g}{6}} = 6 \]

6. **Solve for \( h_{moon} \)**:
Rearranging gives:
\[ h_{moon} = 6h \]

### Final Answer:
The height of the liquid column in the capillary on the surface of the Moon is:
\[ h_{moon} = 6h \]