Two discharge tubes have identical material structure and the same gas is filled in them. The length of one tube is 10cm and that of th other tube is 20cm. Sparking starts in both the tubes when the potential difference between the cathode and the anode is `100 V`. If the pressure in the shorter tube is `1.0 mm` of mercury, what is the pressure in the longer tube?

Explanation

To solve the problem, we will use the relationship between the potential difference (V), pressure (P), and length (D) of the discharge tubes. The key formula we will use is:

\[ V \propto P \times D \]

### Step-by-Step Solution:

1. **Identify Given Values:**
- Length of shorter tube, \( D_s = 10 \, \text{cm} \)
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