Answer:
B) is approximately the same as it would be if all the mass of the sphere were concentrated at the center of the sphere.
Explanation:
Newton’s Law of Universal Gravitation says that if we have two point masses
m and M separated by a distance r, then the mutual force exerted on each is
given by
F = G
mM
r
2
,
where the universal constant is G has approximate value1
G ≈ 6.67 × 10−11N · m2/kg2.
Sometimes, it’s more convenient to measure instead the gravitational field
E resulting from a point with mass M; measured in units of Newtons per kilogram
it measures the force on a point mass (of 1 kg) placed in this field. Therefore,
E will be directed radially inward toward the initial point mass and have a field
strength
E = ||E|| =GMr2,
at a distance r (meters) away from the point with mass M.
For an extended massive object with mass M, not concentrated at a point, the determination of the resulting gravitational field at a given point requires that the contributions of each component particle of mass dM are integrated into a final answer. Newton’s Shell Theorem states essentially two things and has a very important consequence. First of all, it says that the gravitational field outside a spherical shell having total mass M is the same as if the entire mass M is concentrated at its center (center of mass). Secondly, it says that for the same sphere the gravitational field inside the spherical shell is identically 0.
As a consequence of Newton’s shell method, one can conclude immediately that for a spherical homogeneous solid having mass M, the resulting gravitational field is again the same as if the entire mass were concentrated at a point. A somewhat more esoteric consequence is that if the spherical homogeneous object has radius R, then the gravitational field inside the object as a distance r < R from the center is the same as if total mass within a distance r from the center were concentrated at the object’s center.
