A helium balloon has its rubber envelope of weight w_("Rubber") and its is used to lift a weight of w_("Load"). The volume of fully inflated balloon is V_(0). The atmospheric temperature is T_(0) throughout and the atmospheric pressure is known to change with height y according to equation P = P_(0)e^( – ky)where k is a positive constant and P_(0) is atmospheric pres- sure at ground level. The balloon is inflated with sufficient amount of helium so that the net upward force on is F_(0) at the ground level. Assume that pressure inside the balloon is always equal to the outside atmospheric pressure. Density of air and helium at ground level is rho_(a) and rho_(He) respectively. (a) Find the number of moles (n) of the helium in the balloon. For following two questions assume n to be a known quantity. (b) Find the height (y(0)) at which the balloon is fully inflated. (c) Prove that the balloon will be able to rise to height y_(0) if (nRT_(0)g)/(P_(0))(rho_(a)-rho_(Hg)) gt w_("Rubber"+w_("Load")