Question

A hydrogen-filled balloon is used to lift a 120-kg stone off the ground. The basket holding the stone has a mass of 10.0 kg . Part A What must the minimum radius R of the balloon be in order to lift the stone off the ground? Use 1.29 kg/m3 for the mass density of air, and ignore the mass of the hydrogen and the mass of the balloon.

Answer 1

Answer:

Radius, r = 2.88 meters.

Explanation:

It is given that,

A hydrogen-filled balloon is used to lift a 120-kg stone off the ground, m₁ = 120 kg

The basket holding the stone has a mass of 10.0 kg, m₂ = 10 kg

Mass density of air, $d=1.29\ kg/m^3$

We know that buoyant force is equal to the weight of liquid displaced i.e.

$B=mg$

$B=(m_1+m_2)g$

$B=(120+10)\times 9.8$

B = 1274 N

Also, buoyant force is given by :

$B=dVg$

$B=\dfrac{4\pi r^3dg}{3}$

$r^3=\dfrac{3B}{4\pi dg}$

$r^3=\dfrac{3\times 1274}{4\pi \times 1.29\times 9.8}$

$r=2.88\ m$

So, the minimum radius R of the balloon be in order to lift the stone off the ground is 2.88 meters. Hence, this is the required solution.