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The gravitational constant G

The gravitational constant G - where R is the equilibrium...

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The gravitational constant G The strength of the gravitational force depends on the value of G. The value of the gravitational constant can be determined using the Cavendish apparatus. Two small lead spheres of mass m are connected to the end of a rod of length L which is suspended from it midpoint by a fine fiber, forming a torsion balance. Two large lead spheres, each of mass M, are placed in the location indicated in Figure 14.3. The lead spheres will attract each other, exerting a torque on the rod. In the equilibrium position the gravitational torque is just balanced by the torque exerted by the twisted fiber. The torque exerted by the twisted wire is given by Figure 14.3. The Cavendish Apparatus. The torque exerted by the gravitational force is given by
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Unformatted text preview: where R is the equilibrium distance between the center of the large and the small spheres. If the system is in equilibrium, the net torque acting on the rod is zero. Thus All of a sudden the large spheres are rotated to a new position (position B in Figure 14.3). The net torque acting on the twisted fiber is now not equal to zero, and the system will start to oscillate. The period of oscillation is related to the rotational inertia and the torsion constant [kappa] The angle between the two equilibrium positions is measured to be 2[theta]. This, combined with the measured torsion constant, is sufficient to determine the torque [tau] acting on the torsion balance due to the gravitational force. Measurements show that G = 6.67 x 10-11 Nm 2 /kg 2 ....
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