Show that keplerian rotation implies ~ ~ r-1/2. use kepler's third law: p2 ~ ay and assume perfectly circular orbits (i. e. write the rotation speed in terms of p and a) (b) show that a spherically symmetric mass distribution with constant density gives solid body rotation (v = const x r). (set the centripetal force on a star in a circular orbit equal to the gravitational force on that star and substitute for m in terms of the uniform density.)

Which statement is true? a) the work done to lift an object 6 meters is greater than the gravitational potential energy it gains. b) the work required to push an object is less than the work required to pull an object the same distance. c) the work required to raise an object to a height is equal to the gravitational potential energy the object gains. d) the work done against gravity to lift an object straight up is greater than the work required to roll it up a ramp.