A solid sphere of uniform density has a mass of 96 104 kg a

A solid sphere of uniform density has a mass of 9.6 × 10^4 kg and a radius of 3.6 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 6.0 kg located at a distance of (a) 9.2 m and (b) 0.51 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 3.6 m from the center of the sphere.

Solution

a) F = G M m / r²

= (6.67 * 10^-11 * 9.6 * 10⁴ * 6) / (9.2²)

= 4.54 * 10^-7 N

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b) M_in = M r³ / R³ = 9.6 × 10⁴ * 0.51³ / 3.6³

= 272.94 kg

F = G M_in m / r²

= (6.67 * 10^-11 * 272.94 * 6) / (0.51²)

= 4.2 * 10^-7 N

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F_g = G M m / r²