The mercury manometer consists if two unequal arms of equal cross section `1 cm^(2) and lenghths 100cm and 50cm. The two open ends are sealed with air in the tube at a pressure of 80cm of mercurey. Some amount of mercury is now introduced in the manometer through the stopcock connected to it. If mercury rises in the shorter tube to a lenght 10cm in steady state, find the length of the mercury column risen in the longer tube.

Explanation

To solve the problem step by step, we will analyze the situation using the principles of hydrostatics and the ideal gas law.

### Step 1: Understand the System
We have a mercury manometer with two arms of different lengths: one arm is 100 cm long and the other is 50 cm long. The cross-sectional area of both arms is 1 cm². Initially, the pressure of the air sealed in the manometer is 80 cm of mercury.

### Step 2: Initial Conditions
The pressure in both arms before introducing mercury can be denoted as:
- Pressure in shorter arm (P1) = 80 cm Hg
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