A gas- filled freely collapsible balloon is pushed from the surface level of a lake to a depth of `100 m`. Approximately what percentage of its original volume will the balloon finally have? Assume that the gas behaves ideally

Explanation

To solve the problem of how much percentage of the original volume of a gas-filled balloon will remain when pushed to a depth of 100 m in a lake, we can use the principles of gas behavior under pressure, specifically Boyle's Law. Here's a step-by-step solution:

### Step 1: Understand the initial conditions
At the surface of the lake, the pressure (P1) is equal to atmospheric pressure, which is approximately 1 atm (or 101.3 kPa). The volume of the balloon at this point is V (the original volume).

### Step 2: Calculate the pressure at a depth of 100 m
When the balloon is submerged to a depth of 100 m, the pressure increases due to the weight of the water above it. The pressure at a depth (P2) can be calculated using the formula:
\[ P2 = P1 + \rho g h \]
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