question 1 The vector field F(x, y, z) = 2xi + 2yey2+z j +(ey2+z + cos z) k is conservative. Find a

corresponding potential function.

* e raise to power (Y square +z)

Question 2

Consider a solid sphere of radius R, a cylindrical shell of outer radius R, inner radius a,

and height h, and a solid circular cone of radius R and mass M. All three objects have

the same constant density ρ.

(a) Find the moments of inertia about the axis of symmetry for all three objects.

(b) Suppose the objects have the same moments of inertia. Find h and M.

(c) Given the assumptions in part (b), which is heavier, the cone or the sphere?