A mass m is dropped in a tunnel along the diameter of earth from a height `h(ltlt R)` above the surface of earth. Find the time period of motion. Is the motion simple harmonic?

Explanation

To solve the problem of a mass \( m \) dropped in a tunnel along the diameter of the Earth from a height \( h \) (where \( h \ll R \), with \( R \) being the radius of the Earth), we will follow these steps:

### Step 1: Determine the time taken to fall from height \( h \) to the surface of the Earth.

When the mass is dropped from height \( h \), it will fall freely under the influence of gravity. The equation of motion can be used here:

\[
S = ut + \frac{1}{2} a t^2
...