Chapter 12

A planet is in a circular orbit about a remote star, far from any other object in the universe. Which of the following statements is true? a) There is only one force acting on the planet. b) There are two forces acting on the planet and their resultant is zero. c) There are two forces acting on the planet and their resultant is not zero. d) None of the above statements are true.

Two 30.0 -kg masses are held at opposite corners of a square of sides $20.0\mathrm{cm}.$ If one of the masses is released and allowed to fall toward the other mass, what is the acceleration of the first mass just as it is released? Assume that the only force acting on the mass is the gravitational force of the other mass. a) $1.5\cdot {10}^{-8}\mathrm{m}/{\mathrm{s}}^2$ b) $2.5\cdot {10}^{-8}\mathrm{m}/{\mathrm{s}}^2$ c) $7.5\cdot {10}^{-8}\mathrm{m}/{\mathrm{s}}^2$ d) $3.7\cdot {10}^{-8}\mathrm{m}/{\mathrm{s}}^2$

With the usual assumption that the gravitational potential energy goes to zero at infinite distance, the gravitational potential energy due to the Earth at the center of Earth is a) positive. b) negative. c) zero. d) undetermined.

A man inside a sturdy box is fired out of a cannon. Which of following statements regarding the weightless sensation for the man is correct? a) The man senses weightlessness only when he and the box are traveling upward. b) The man senses weightlessness only when he and the box are traveling downward. c) The man senses weightlessness when he and the box are traveling both upward and downward. d) The man does not sense weightlessness at any time of the flight.

In a binary star system consisting of two stars of equal mass, where is the gravitational potential equal to zero? a) exactly halfway between the stars b) along a line bisecting the line connecting the stars c) infinitely far from the stars d) none of the above

Two planets have the same mass, $M,$ but one of them is much denser than the other. Identical objects of mass $m$ are placed on the surfaces of the planets. Which object will have the gravitational potential energy of larger magnitude? a) Both objects will have the same gravitational potential energy. b) The object on the surface of the denser planet will have the larger gravitational potential energy. c) The object on the surface of the less dense planet will have the larger gravitational potential energy. d) It is impossible to tell.

Two planets have the same mass, $M.$ Each planet has a constant density, but the density of planet 2 is twice as high as that of planet $1.$ Identical objects of mass $m$ are placed on the surfaces of the planets. What is the relationship of the gravitational potential energy, $U_1,$ on planet 1 to $U_2$ on planet $2?$ a) $U_1=U_2$ b) $U_1=\frac{1}{2}{U}_2$ c) $U_1=2U_2$ d) $U_1=8U_2$ e) $U_1=0.794U_2$

For two identical satellites in circular motion around the Earth, which statement is true? a) The one in the lower orbit has less total energy. b) The one in the higher orbit has more kinetic energy. c) The one in the lower orbit has more total energy. d) Both have the same total energy.

Which condition do all geostationary satellites orbiting the Earth have to fulfill? a) They have to orbit above the Equator. b) They have to orbit above the poles. c) They have to have an orbital radius that locates them less than $30,000\mathrm{km}$ above the surface. d) They have to have an orbital radius that locates them more than $42,000\mathrm{km}$ above the surface.

Can the expression for gravitational potential energy $U_{\mathrm{g}}(y)=mgy$ be used to analyze high-altitude motion? Why or why not?