Consider a thin hollow fixed spherical shell of radius R and surface mass density rho. A particle initially at rest falls in from infinity. What is its speed when it reaches the center of the shell?
(Assume that a tiny hole has been cut in the shell to let the particle thru.)
rho, distance between centers of masses, R, G
F = -GMm/r^2
The Attempt at a Solution
The source of the force acts through the center of the sphere, right? So I know the force, but the problem says the particle falls from infinity (I'm assuming I'd need to use calculus here then)
The gravitational force from the sphere acting on the particle is originating from the sphere's center of mass, and pulling it towards that center radially. The part that tricks me is bringing the test particle in from infinity, so the g-force is pretty much zero at that point in time, and slowly increases at it gets closer. Seems like I require an infinite sum here, but not sure how to realize that.