Question

6. A helium balloon is designed to lift a load of 400 kg. Find the radius of this balloon?

Answer 1

Since density of Helium is less than the density of air , force of buoyancy will be more than the gravitational force on the ballon.

$\rho_{air}Vg-\rho_{He}Vg=400g$

$\rho_{air}V-\rho_{He}V=400$

$(\rho_{air}-\rho_{He})\frac{4}{3}\pi R^3=400$

$R=\left ( \frac{400}{(\rho_{air}-\rho_{He})\frac{4}{3}\pi} \right )^{1/3}$

$R=\left ( \frac{400}{(1.29-0.179)\frac{4}{3}\pi} \right )^{1/3}=4.41\,m$

Radius of balloon is $\boxed{R=4.41\,m}$