In terms of polar coordinates, the force exerted on an object of mass m by the gravity of...

In terms of polar coordinates, the force exerted on an object of mass m by the gravity of a hypothetical two-dimensional planet is F = – (mgTRT/r)er where gT is the acceleration due to gravity at the surface, RT is the radius of the planet, and r is the distance of the object from the center of the planet.

(a) Determine the potential energy associated with this gravitational force.

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(b) If the object is given a velocity v0 at a distance r0. what is its velocity v as a function of r?