If the particle of mass m1 is located at a distance of r outside a solid homogenous sphere of radius R and mass m2, the solid sphere attracts the mass as if all the mass of the sphere were concentrated at its center. If the particle of mass m1 is located inside the uniform solid sphere, then the force on m1 is due solely to the mass m-2-prime contained within the sphere of radius r, where r is the distance that separates the particle m1 from the center of sphere m2. Newton's law of gravitation applies, with masses m1 and m2 prime. Newton's law of gravitation applies here when the particle is outside the sphere. In this case, the force of attraction on the particle is equal to the gravitational constant, G, times the product of m1 and m2 divided by r-squared. When the particle is inside the sphere, Newton's law applies to the particle and the portion m2-prime of the mass of the sphere with a radius r, representing the distance between the particle and the center of the sphere. Here, the force of attraction on the particle is equal to G times the product of m1 and m2-prime divided by r-squared. If a particle is located inside a solid sphere of density rho and radius R that is not uniform, then the mass m2 prime in the last equation is equal to the integral of rho times dV With the integration taken over the volume of the dotted surface of radius small r. Let us do an example. Consider a uniform sphere of mass 10 kilograms, and radius 1 meter. Find the magnitude of the force on a particle of mass 20 grams located at point A, 5 meters away from the center of the sphere, and particle of the same mass at point B on the surface of the sphere. ... Now let us see what the gravitational pull is on an object inside the sphere. What is the force on a particle of mass 20 g, inside the sphere 0.4 meters radially inward from the surface? ... First, let's determine the mass m-two-prime of the sphere ecnlosed between the particle and the center of the circle. Because the sphere is homogeneous, m-two-prime over m-two is equal to the volume of the enclosed sphere over the total volume of the sphere. Since the volume of the sphere is four thirds times Pi multiplied by the radius cubed, m-two-prime over m-two is equal to the ratio of the cubes of the radii. The mass m-two-prime of the sphere is thus given by the ratio of the cube of the radii multiplied by m-two. From Newton's law, the gravitational force on the particle inside the sphere is equal to capital G times the product of m-one and m-two-prime divided by r-squared where the radius r, represents the distance between the particle and the center of the spere. Substituting m-two-prime from the previous relation, and simplifying we find that the force is equal to Gtimes the product of m one and m two times the radius r divided by the radius of the sphere R cubed. divided by the radius of the sphere R cubed.

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