A ball is released in a smooth dimetrical tunnel of earth
a. After how much time will it pass through the center of earth?
b. With what speeed will the ball pass the center earth?

Explanation

To solve the problem of a ball released in a smooth diametrical tunnel through the Earth, we will break it down into two parts:

### Part a: Time to Pass Through the Center of the Earth

1. **Understanding the Forces**: When the ball is released, it experiences gravitational force towards the center of the Earth. The gravitational force inside the Earth varies linearly with distance from the center.

2. **Acceleration Inside the Earth**: The acceleration \( a \) of the ball at a distance \( r \) from the center of the Earth is given by:
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