onsider a planet consisting of two thin concentric shells, as in the picture, both made from the same material (same mass density). The radii R1 and R2 are given, and the thickness of the inner shell, d1 is also given. Using the shell theorem, determine the required thickness d2 of the outer shell so that the magnitude of the gravitational field for people living on the outside of the outer shell is the same as that for people living on the outside of the inner shell. You can assume that the thicknesses d1, d2 are negligible in comparison with the radii R1, R2.
Consider a planet consisting of two thin concentric shells, as in the picture, both made from the same material (same mass density). The radii R1 and R2 are given, and the thickness of the inner shell, d1 is also given. Using the shell theorem, determine the required thickness d2 of the outer shell so that the magnitude of the gravitational field for people living on the outside of the outer shell is the same as that for people living on the outside of the inner shell. You can assume that the thicknesses d1, d2 are negligible in comparison with the radii R1, R2.
The shell theorem states that a spherically body affects external objects gravitationally as if all of its mass was concentrated at its center.
Also, If a body is a spherical shell ,no net gravitational force is exerted by the shell on any object inside, regardless of the object's location inside.
We will start by finding the mass of the two shells and then find the field on surfaces of each shell.
Here we assume that the mass density of shells as .
Step by step
Solved in 3 steps with 3 images
