A spherical air bubble is rising from the depth of a lake when pressure is `P atm` and temperature is `T K`. The percentage increase in the radius when it comes to the surface of a lake will be (Assume temperature and pressure at the surface to be, respectively, `2T K` and `P//4`.)

Options

A. `100%`
B. `50%`
C. `40%`
D. `200%`

Explanation

To solve the problem of the percentage increase in the radius of a spherical air bubble as it rises from the depth of a lake to the surface, we can follow these steps:

### Step 1: Understand the conditions at depth and surface
- At depth:
- Pressure, \( P_1 = P \) atm
- Temperature, \( T_1 = T \) K
- At surface:
- Pressure, \( P_2 = \frac{P}{4} \) atm
...