find the acceleration due to gravity at the centre of a solid hemisphere.
The Attempt at a Solution
i decided to go for cylindrical coordinayes (which is way beyond my syllabus). I did some research though.
let me take a point P(r,θ,z) inside the sphere amd an elemental volume dV at P. This P exerts a force dF. But there is also a point Q(r,θ+180°,z) which cancells out the horizontal component of dF. let the line OP make an angle φ with the Z axis. (assuming the hemisphere lies on the xy plane with centre at O)
Is this expresion for dV true for all cases? how do you get that expression for dV?
(i found that expression on some video).
now i have to integrate the expression.
im finding it difficult to find upper limit for z.