A Tunnel so long!

Consider the earth as a uniform sphere of mass MM And Radius RR. Imagine a straight smooth tunnel made through the earth which connects any two points on its surface (The two points are not diametrically opposite). Determine the time that a particle would take to go from one end to the other through the tunnel. If Your answer is TsT s, then find the value of T100\frac{T}{100} to the nearest integer.

Details And Assumptions:

  • Consider only gravitation force due to earth be acting on the particle during its motion along the tunnel.

  • Take acceleration due to gravity on surface of Earth = 10ms210ms^{-2}

  • Radius of Earth = 6400km6400 km.

This is an entry for the problem writing party.

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