A sphere of radius R has its centre at the origin. It has a uniform mass density ro except that there is a spherical hole of radius r = R/2 whose centre is at x = R/2 as in fig. (a) Find gravitational field at points on the axis for |x| > R. (b) Show that the gravitational field inside the hole is uniform, find its magnitude and direction.

Question

G1 Physics · Accepted Answer

Step 1: Apply the shell theorem. Inside a uniform spherical shell the field is zero; inside a uniform solid sphere only the enclosed mass contributes. Step 2: Superpose the fields of the solid sphere and shells/cavity with correct signs. Step 3: Equate the fields at the stated points or evaluate the requested ratio. Final: A: (a) g(x)= (πGρ₀R³/6)[1/(x-R/2)² - 8/x²] along the axis; (b) g = -(2πGρ₀R/3)𝐢 inside the cavity.