Two vessels of the same volume and filled with the same gas at the same temperature. If the pressure of the gas in these vessel be in the ratio 1:2, then state : (i) the ratio of the rms speeds of the molecules, (ii) the ratio of the number of molecules.

Explanation

To solve the problem, we need to analyze the relationship between pressure, temperature, volume, and the number of molecules in the context of the kinetic theory of gases.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- We have two vessels (V1 and V2) of the same volume (V).
- Both vessels contain the same gas at the same temperature (T).
- The pressure in the first vessel (P1) is in the ratio of 1 to the pressure in the second vessel (P2), i.e., P1:P2 = 1:2.
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