How much would a simple pendulum deflect due to the gravity of a nearby mountain?$$ As a model of a large mountain, use a sphere of radius R $=2\mathrm{.}3$ km and mass density $=3000$ kg$/$m$3.$ If a small mass is hung at the end of a string of length $0\mathrm{.}50$ m at a distance of $3\mathrm{.}9$ R from the center of the sphere $($and assuming the sphere pulls in a horizontal direction on the hanging mass$),$ how far would the small hanging mass deflect under the influence of the sphere's gravitational force?

Your answer should be in$$m $($micrometers$,10-6$ m$)$:

$$x$=$m$$