# Calculating the gravitational field due to a horizontal uniform thin disk

1. Mar 6, 2012

### AaronKnight

1. The problem statement, all variables and given/known data
Show that the gravitational field due to a horizontal uniform thin disc (thickness D, radius R and density r) at a distance h vertically above the centre of the disc has magnitude

2πGρd(1-h/(R2+h2)1/2)

A pendulum clock in the centre of a large room is observed to keep correct time. How many
seconds per year will the clock gain if the floor is covered by a 1cm thick layer of lead of density
11350kgm−3?
[Newton’s gravitational constant is G = 6.67×10−11Nm2 kg−2.]

2. Relevant equations
Gravitational potential, $\phi$=-Gdm/R
Where dm=2πRDρ.dR
Gravitational field, g= -$\nabla$$\phi$

3. The attempt at a solution
I have got to $\phi$=-2πDρGdR and I know I need to integrate with respect to R, then use the g= -$\nabla$$\phi$ but I am unsure what my integration limits should be? I think I need to integrate between 0 and R but then I can't see how I would get the h/(R2+h2)1/2 term?
Any hints would be very useful.

2. Mar 6, 2012

### AaronKnight

In the relevant equations sections ϕ=-Gdm/R should be dϕ=-Gdm/R