A glass rod of radius `r_(1)` is inserted symmetrically into a vertical capillary tube of radius `r_(2)` such that their lower ends are at the same level. The arrangement is now dipped in water. Find the height to which water will rise in to the tube.
(S = surface tension of water, d= density of water).

Explanation

To find the height to which water will rise in the capillary tube when a glass rod is inserted into it, we can follow these steps:

### Step 1: Understand the Forces Acting on the Water
The upward force acting on the water due to surface tension can be expressed as:
\[ F_{\text{up}} = \text{Surface Tension} \times \text{Perimeter} \]
The perimeter of the glass rod and the capillary tube contributes to this force. The total upward force due to surface tension is given by:
\[ F_{\text{up}} = S \times (2\pi r_1 + 2\pi r_2) \]
where \( S \) is the surface tension of water, \( r_1 \) is the radius of the glass rod, and \( r_2 \) is the radius of the capillary tube.
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