A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of $0\mathrm{.}650m^3$ and the tension in the cord is $1120N.$

a$)$ Calculate the buoyant force exerted by the water on the sphere, and hence, find the mass of the sphere.

b$)$ The cord breaks and the sphere rises to the surface. When the sphere comes to rest, determine the fraction of its volume that will be submerged.