The gravitational attraction due to a nearby mountain range might be expected to cause a plumb bob to hang at an angle slightly different from the vertical. If a mountain range could be represented by an infinite half-cylinder of radius a and density rho lying on a flat plane (see picture below), show that a plumb bob at a distance r0 from the cylinder axis would be deflected by an angle θ ≈ πa2Grho/(r0 g). You can assume that θ ≪ 1 and r0 ≫ a. Hint: Gauss’ law is useful. In actual measurements of this effect, the observed deflection is much smaller. Next assume that the mountain range can be represented by a cylinder of radius a and density rho which is floating in a fluid of density 2rho as illustrated. Show that the plumb-bob deflection due to the mountain range is zero in this model. Since the latter result is in much better agreement with observations, it is postulated that mountains, and also continents, are in isostatic equilibrium with the underlying mantle rock.