$(1\mathrm{.}5$ points$)$ A sphere completely submerged in water is tethered to the bottom with a string. a$.$ Draw a FBD for the sphere and write Newton$$s $2$nd Law for the sphere. b$.$ The tension in the string is one$-$third the weight of the sphere. Use the equation for the buoyancy force and the $2$nd Law equation from part $($a$)$ to find the density of the sphere. c$.$ If the sphere were submerged in oil instead of water, what happens to the $($i$)$ buoyancy force on the sphere, $($ii$)$ the weight of the sphere and $($iii$)$ the tension in the string? This is a thinking and reasoning question, not a math question.