A balloon whose volume is 300m3 is filled with hydrogen. If the density of air is 1.3 kgm-3, find the upthrust on the balloon. [g = 10ms-2]
Answer Details
To find the upthrust on the balloon, we need to use the Archimedes' principle which states that an object submerged in a fluid experiences an upward force that is equal in magnitude to the weight of the fluid displaced. In this case, the balloon is not submerged but is filled with hydrogen which is lighter than air. Thus, the upthrust on the balloon is equal to the weight of the air displaced by the balloon.
The weight of the air displaced by the balloon is given by the difference between the weight of the air that would fill the same volume as the balloon and the weight of the hydrogen that actually fills the balloon.
The weight of air that would fill the same volume as the balloon is given by:
mass of air = density of air x volume of balloon
mass of air = 1.3 kg/m^3 x 300 m^3
mass of air = 390 kg
The weight of the hydrogen that fills the balloon is given by:
mass of hydrogen = density of hydrogen x volume of balloon
mass of hydrogen = 0.09 kg/m^3 x 300 m^3
mass of hydrogen = 27 kg
Therefore, the weight of the air displaced by the balloon is:
weight of air = mass of air x acceleration due to gravity
weight of air = 390 kg x 10 m/s^2
weight of air = 3900 N
The upthrust on the balloon is equal to the weight of the air displaced, which is 3900 N. Therefore, the correct answer is "3900N."
Explanation:
The upthrust on an object in a fluid is equal to the weight of the fluid displaced by the object. In this case, the balloon filled with hydrogen displaces air, which has a known density. By calculating the weight of air displaced and subtracting the weight of the hydrogen filling the balloon, we can find the upthrust on the balloon. By using the given values and applying Archimedes' principle, we find that the upthrust on the balloon is 3900 N. Therefore, the correct answer is "3900N."