**Birth of a Supernova**.

A spherical star of mass $M$ and radius $R$ isin a final step to be a supernova.In this process the star produce a large ammount of heat energy.As a result,the size of the star increases rapidly.Let assume the readius of the star becomes $100R$ .For simplicity we assume that density is uniform all the time.

(a)Find the total energy of the star at the initial and the final condition.

(b)Find the heat energy produced by the star.Let the star radiates heat exponentially as $E(y)=Ae^{-y} $.[Here $E(y)$ is the radiation rate at year $y$ ] It takes $y$ year to radiate all the energy produced. (when it was becoming a supernova)

(c) Find $A$.