A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the center of the tunnel.

Find the Graviational Force and a depth d...You will observe it is zero at the centre and directly proportional to the distance from the centre up and until the surface of the earth...after with the value decreases exponentially..

So..when th particle is x distance away form the centre,force of attraction is only due to the part that is having a radius x.Hence find the mass of that portion...M earth/ volume earth *Volume of sphere of radius x gives you its mass..Then just apply equation for gravitational force,replacing the second mass from above...Please review you reference book or guide,as this is a very basic theory :)

zacky