A particle is dropped from a height equal to the radius of the earth above the tunnel dug through the earth as shown in the figure.
 $R$ : Radius of earth.
$M$ : Mass of earth.

 

Particle will oscillate through the earth to a height R on both sides.

Motion of the particle is periodic.

Particle will execute simple harmonic motion.

Particle passes the centre of earth with a speed $=\sqrt{\frac{2\text{GM}}{\text{R}}}.$