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Chapter 13: Q21P (page 380)
Certain neutron stars (extremely dense stars) are believed to be rotating at about. If such a star has a radius of, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?
Mass of the material on the surface of the neutron star is
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Three point particles arefixed in position in anx-yplane. Twoof them, particleAof mass 6.00 gand particleBof mass 12.0 g, are shown in the figure, with a separation ofatangle.ParticleC, with mass, 8.00 g is not shown. The net gravitational forceacting on particleAdue to particlesBandCisat an angleof from the positive direction of thexaxis. What is (a) thexcoordinate and (b) theycoordinate of particleC?
As seen in the figure, two spheres of massmand a third sphere of massMform an equilateral triangle, and a fourth sphere of massis at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero. (a) What isMin terms ofm? (b) If we double the value of, what is the magnitude of the net gravitational force on the central sphere?
The presence of an unseen planet orbiting a distant star can sometimes be inferred from the motion of the star as we see it. As the star and planet orbit, the center of mass of the star-planet system, the star moves toward and away from us with what is called the line of sight velocity, a motion that can be detected. Figure 13-49 shows a graph of the line of sight velocity versus time for the star . The star鈥檚 mass is believed to be of the mass of our Sun. Assume that only one planet orbits the star and that our view is along the plane of the orbit. Then approximate (a) the planet鈥檚 mass in terms of Jupiter鈥檚 mass and
(b) the planet鈥檚 orbital radius in terms of Earth鈥檚 orbital radius .
A solid uniform sphere has amass ofand a radius of. What is the magnitude of the gravitational force due to the sphere on a particle of massmlocated at a distance of(a) 1.5 m and (b) 0.50 m from the center of the sphere? (c) Write a general expression for the magnitude ofthe gravitational force on the particle at a distancefrom the center of the sphere.
The three spheres in Fig. 13-45, with masses, , and , have their centers on a common line,with and . You move sphereBalong the lineuntil its center-to-center separation fromCis . Howmuch work is done on sphereB(a) by you and (b) by the net gravitational force onBdue to spheresAandC?
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