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, [itex]\phi[/itex]=-Gdm/R Where dm=2πRDρ.dR Gravitational field, g= -[itex]\nabla[/itex][itex]\phi[/itex] 3. The attempt at a solution I have got to [itex]\phi[/itex]=-2πDρGdR and I know I need to integrate with respect to R, then use the g= -[itex]\nabla[/itex][itex]\phi[/itex] 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.