Assume the earth is a uniform sphere of mass M and radius R. As strange as it may sound, if one can dig a long tunnel from one side of the Earth straight through the center and exit the other end, any object falling into the tunnel will appear at the other end (i.e. the opposite side of the Earth) in just 2530 s (42.2 min). Call that time t. Let t be a function of G, M, and R, where G = 6.67 x 10^-11 m3 kg−1 s−2 is the Universal Gravitational Constant, M = 5.98 x 10^24 kg, and R = 6400 km. (a) From dimensional analysis alone find the expression for t, up to a numerical constant c. (b) Determine the value of c by using the above values in the expression found in part (a)

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.