A tunnel is drilled from the surface of a planet straight down to its antipodal point on the other side of the planet. A particle at the surface is dropped from rest into the tunnel. Denote the position of the particle from the planet’s center at time t by r(t). Assume that the gravitational force the particle experiences is due only to the mass of the planet within the sphere of radius r(t). Calculate the time (in seconds) the particle will take to reach the other end of the planet. Let the radius of the entire planet be R = 20 × 106 m and take 4.9 as the value of g

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.