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A string is wrapped around a uniform disk of mass M - 1-5 kg and radiu.docx
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### A solid sphere of uniform density has a mass of 6-6 104 kg and a radi.docx

1. A solid sphere of uniform density has a mass of 6.6 Ã— 104 kg and a radius of 0.51 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 6.2 kg located at a distance of (a) 1.5 m and (b) 0.096 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r ? 0.51 m from the center of the sphere. a) 1.2e-5 b) ? c) | F on m | = K*r, where K = ? Solution (a) F = GMm/r 2 = 6.673*10 -11 *6.6*10 4 *6.2/1.5 2 = 1.2136*10 -5 N (b) M inside = M*r inside 3 /R 3 = 6.6*10 4 *0.096 3 / 0.51 3 M inside = 440.2 kg F = GM inside m/r 2 = 6.673*10 -11 *440.2*6.2/0.096 2 = 1.98*10 -5 N (c) F = GM inside m/r 2 = G* M*r inside 3 /R 3 *m/r 2 F = GM/R 3 *r inside where , K = GM/R 3 = 6.673*10 -11 *6.6*10 4 / 0.51 3 K = 3.32*10 -5
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