An aluminum plate fixed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of `10^@C`.The temperature of the entire system is slowly increased. At what temperature will the ball fall down? coefficient of linear expansion of aluminum is `23 xx 10^(-6)C^(-1)` and that of steel is `11 xx 10^(-6)C^(-1)`.

Explanation

To solve the problem, we need to determine the temperature at which the diameter of the steel sphere equals the diameter of the aluminum hole. We will use the coefficients of linear expansion for both materials to find this temperature.

### Step 1: Define the known values
- Diameter of the aluminum hole, \( D_{Al} = 2.000 \, \text{cm} \)
- Diameter of the steel sphere, \( D_{steel} = 2.005 \, \text{cm} \)
- Coefficient of linear expansion of aluminum, \( \alpha_{Al} = 23 \times 10^{-6} \, \text{°C}^{-1} \)
- Coefficient of linear expansion of steel, \( \alpha_{steel} = 11 \times 10^{-6} \, \text{°C}^{-1} \)
- Initial temperature, \( T_0 = 10 \, \text{°C} \)
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