Aspherical balloon is made from a material whose mass is 3.00 kg. the thickness of the material is negligible compared to the 1.50 m radius of the balloon. the balloon is filled with helium at a temperature of 305 k and just floats in air, neither rising nor falling. the density of the surrounding air is 1.19 kg/m3. find the pressure of the helium gas assuming it is ideal.

To solve the problem it is necessary to apply the definition of Newton's second Law and the definition of density.

Density means the relationship between volume and mass:

While Newton's second law expresses that force is given by

F = ma

Where,

m = mass

a= acceleration (gravity at this case)

In the case of the given data we have to,

In equilibrium, the entire system is equal to zero, therefore

Where,

Weight of balloon

Weight of helium gas

Bouyant force

Then we have,

Replacing the values we have that

Now by ideal gas law we have that

But the relation \frac{n}{m} is equal to the inverse of molar mass, that is

Therefore the pressure of the helium gas assuming it is ideal is 0.61Mpa

it has to be b, about 97 percent.