The sensitivity of a level tube refers to how easily it can detect small changes in the level of liquid. In other words, it is a measure of how responsive the tube is to changes in the liquid level.

The correct answer to the question is option 'D', which states that the sensitivity of a level tube decreases when viscosity and surface tension are increased. Let's understand why this is the case:

1. Viscosity:
Viscosity is a measure of a fluid's resistance to flow. When the viscosity of the liquid in the level tube increases, it becomes thicker and flows more slowly. This increased viscosity makes it harder for the liquid to respond to small changes in level, resulting in a decrease in sensitivity. As a result, the level tube becomes less effective at detecting small changes in the liquid level.

2. Surface Tension:
Surface tension is a property of liquids that causes the surface to behave like a stretched elastic sheet. It is the force that holds the molecules of a liquid together at the surface. When the surface tension of the liquid increases, it forms a stronger bond between the liquid and the inner surface of the level tube. This increased surface tension makes it more difficult for the liquid to move freely and respond to small changes in level. As a result, the sensitivity of the level tube decreases.

3. Other options:
The other options given in the question do not directly affect the sensitivity of the level tube.

- Radius of Curvature of Inner Surface: The radius of curvature of the inner surface of the level tube does not directly affect its sensitivity. It may affect the overall shape of the meniscus formed by the liquid, but it does not impact the ability of the level tube to detect small changes in level.

- Diameter of Tube: The diameter of the level tube also does not directly affect its sensitivity. It may affect the volume of liquid required to cause a noticeable change in level, but it does not impact the responsiveness of the tube to small changes in level.

- Length of Tube: Similarly, the length of the level tube does not directly affect its sensitivity. It may affect the overall height of the liquid column, but it does not impact the ability of the tube to detect small changes in level.

In conclusion, the sensitivity of a level tube decreases when the viscosity and surface tension of the liquid increase. This is because increased viscosity and surface tension make it harder for the liquid to respond to small changes in level, resulting in a decrease in sensitivity.