Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. The motion of the particle as seen from the earth is
As the force is acting towards the center of the Earth. The path must be straight line and along the diameter of the circle.
Therefore, Option (c) is correct.
The Gravitational Force acting on the particle is given by the equation.
As this force is not linearly dependent on displacement so it cannot be harmonic simple harmonic motion, because for simple harmonic motion.
F 
So it's not a simple harmonic motion
Therefore,
Option (a). is incorrect.
Since, Particle used to go and then returns to the same position and all this occurs in a fixed time which is numerically equal to 84.6 minutes.
Thus, it is Periodic Motion.
Hence,
Option (d). is correct.
Therefore, option C and D are correct.