If the earth were a homegeneous sphere and a straight hole was bored in it through its centre, so when a body is dropped in the hole, it will excutes SHM. Determine the time period of its oscillation . Radius of the earth is `6.4 xx 10^(5)` m and `g=9.8 ms^(-2)`

Explanation

To determine the time period of oscillation for a body dropped into a straight hole bored through the center of a homogeneous Earth, we can use the principles of simple harmonic motion (SHM).

### Step-by-Step Solution:

1. **Understanding the Force Acting on the Body:**
When a body is dropped into the hole, the gravitational force acting on it will vary with the distance from the center of the Earth. According to the shell theorem, the gravitational force inside a uniform sphere is directly proportional to the distance from the center.

The gravitational force \( F \) acting on the body at a distance \( r \) from the center of the Earth can be expressed as:
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