7. (a) The pressure difference results in forces applied as shown in the figure. We consider a team of horses pulling to the right. To pull the sphere apart, the team must exert a force at least as great as the horizontal component of the total force determined by “summing” (actually, integrating) these force vectors. We consider a force vector at angle θ. Its leftward component is Δpcos dA, where dAis the area element for where the force is applied. We make use of the symmetry of the problem and let dAbe that of a ring of constant on the surface. The radius of the ring is r= Rsin , where Ris the radius of the sphere. If the angular width of the ring is
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