Consider a thin disc of radius R and consisting of a material with constant mass density(per unit of area) g. Use cylindrical coordinates, with the z-axis perpendicular to theplane of the disc, and the origin at the disc's centre. We are going to calculate thegravitational potential, and the gravitational field, in points on the z-axis only.the gravitational potential p(2) set up by that disc is given bydr';()² + z²sp(2) = 27Gg Using a symmetry argument, explain why, for points on the positive z-axis, thegravitational field points towards the centre of the disk, i.e. parallel to the z-axis.Starting from the gravitational potential, and using the answer to 4., derive anexpression for the gravitational field a for points on the positive z-axis.What does this become in the limit R → ?(Brain teaser) Show that the potential o “becomes infinite" in that same limit. Howcan you get round this problem, to find the gravitational field from the potentialeven in the limit R→ 0?

The gravitational potential set up by the disk is given as : φ(z)=2πGϱ∫0R r'r'2+z2dr'Integrating…

Answered: Using a symmetry argument, explain why,…

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