$[$Pressure & Force$]$ A kid buys a helium balloon. The volume of the balloon is $0\mathrm{.}1m^3$ and

the surface area of the balloon is $0\mathrm{.}25m^2.$ While playing with the balloon, he released the

string and the balloon went up $100$ m $.$ The balloon changed in size and the surface area

became $0\mathrm{.}4m^2.$ Assume average constant density of air $(=1\mathrm{.}1k\frac{g}{m^3}).$ Take atmospheric

pressure on the ground to be $100$kPa.$g=9\mathrm{.}81\frac{m}{s^2}.$ Find:

$($a$)$ Total force exerted by the balloon on helium at the ground level.

$(25\mathrm{.}00kN)$

$($b$)$ Pressure of air inside the balloon at $100$ m altitude.

$($c$)$ Total force exerted by helium on the balloon at $100$ m altitude.

$(24\mathrm{.}73kN)$