Which condition must be met for a balloon to float in air?

• A. The weight of the balloon must be less than the buoyant force acting on it. $W<F\_b$
• B. The density of the balloon material must be greater than the density of air. $\rho \_\mathrm{balloon}>\rho \_\mathrm{air}$
• C. The pressure inside the balloon must equal the atmospheric pressure. $P\_\mathrm{inside}=P\_\mathrm{atm}$
• D. The temperature inside the balloon must be lower than the temperature outside. $T\_\mathrm{inside}<T\_\mathrm{outside}$

Answer: (A)

Verified step by step guidance

1. Understand that for a balloon to float, the upward buoyant force must overcome the downward gravitational force (weight) acting on the balloon.
2. Recall that the buoyant force \(F_b\) is equal to the weight of the air displaced by the balloon, which can be expressed as \(F_b = \rho_{air} \times V \times g\), where \(\rho_{air}\) is the density of air, \(V\) is the volume of the balloon, and \(g\) is the acceleration due to gravity.
3. The weight of the balloon \(W\) is given by \(W = m \times g\), where \(m\) is the mass of the balloon including the gas inside it and the balloon material.
4. For the balloon to float, the condition \(W < F_b\) must be satisfied, meaning the total weight is less than the buoyant force.
5. Note that this implies the average density of the balloon (including the gas inside) must be less than the density of the surrounding air, so \(\rho_{balloon} < \rho_{air}\).