The end of a capillary tube with a radius `r` is immersed in water. Is mechanical energy conserved when the water rises in the tube? The tube is suficiently long. If not calculate the energy change.

Explanation

To determine whether mechanical energy is conserved when water rises in a capillary tube, we can analyze the forces and energy changes involved in the process. Here’s a step-by-step solution:

### Step 1: Understand the Forces Involved
When the capillary tube is immersed in water, the water rises due to the balance between the surface tension force and the weight of the water column inside the tube. The surface tension force (Fs) can be expressed as:
\[ F_s = \gamma \cdot L \]
where \( \gamma \) is the surface tension and \( L \) is the length of the contact line, which for a circular tube is \( 2\pi r \).

### Step 2: Calculate the Weight of the Water Column
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