F=ma 2024 Problem 22

Physics · mechanics

Problem

Question: A spherical shell is made from a thin sheet of material with a mass per area of

\sigma

. Consider two points,

P_1

and

P_2

, which are close to each other, but just inside and outside the sphere, respectively. If the accelerations due to gravity at these points are

g_1

and

g_2

, respectively, what is the value of

|g_1 - g_2|

? (A)

\pi G\sigma

. (B)

4\pi G\sigma /3

. (C)

2\pi G\sigma

. (D)

4\pi G\sigma

. (E)

8\pi G\sigma