Question

A spherical weather balloon is filled with hydrogen until its radius is 3.00 m. its total mass including the instruments it carries is 11.0 kg. (a) find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3.

Answer 1

The buoyant force is equal to the weight of air displaced by the balloon:

$B=\rho V g$

where

$\rho=1.29 kg/m^3$ is the air density

V is the volume of the balloon

$g=9.81 m/s^2$ is the gravitational acceleration

We need to find the volume of the balloon. Its radius is r=3.00 m, so its volume is

$V=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (3.0 m)^3=113.04 m^3$

And by substituting this into the previous equation, we find the buoyant force acting on the balloon:

$B=\rho V g=(1.29 kg/m^3)(113.04 m^3)(9.81 m/s^2)=1430.5 N$