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Assertion: A hydrogen-filled balloon stops rising after it has attained a certain height in the sky.Reason: The atmospheric pressure decreases with height and becomes zero when the maximum height is attained.A) If both assertion and reason are true and reason is the correct explanation of assertion.B) If both assertion and reason are true but reason is not the correct explanation of assertion.C) If the assertion is true but the reason is false.D) If assertion and reason both are false.

Last updated date: 16th Sep 2024
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Hint To answer this question, we have to apply the concepts of buoyancy. The relative density of an object compared to the medium in which it is placed decides whether the object will float or sink. A less dense object in a denser medium will float and vice versa.

Complete step by step answer
The hydrogen-filled balloon initially rises in the air because the weight of the displaced air i.e., upthrust is greater than the weight of the hydrogen and the balloon. This force is similar to the force experienced when an empty container is dipped in water.
The difference in densities causes the less dense object to be pushed above. Since the density of air decreases with height therefore the balloon halts at a particular height. At this particular point, the density of the air will be equal to the density of the hydrogen inside the balloon.
The force acting on the balloon downwards that is the weight of the balloon will be balanced by the buoyant force acting on the balloon at this particular point. Hence the net force acting on the balloon will be cancelled out and the balloon stops rising.
So, the assertion is correct. However, the reason is incorrect since the atmospheric pressure does not reach zero at that height. It just decreases such that the density of the atmosphere equals the density of the hydrogen inside the balloon.
Hence the correct choice is option (C).

Note
Here, we can treat the hydrogen inside the balloon as a liquid to apply the principles of buoyancy. Hydrogen is less dense than air at the ground i.e., at atmospheric pressure near the ground so it will rise up. Atmospheric pressure decreases with height as Earth’s gravity gets weaker with increasing height. However, hydrogen balloons are so light that they can be easily displaced by the wind in which case the dominant force will be the wind of the balloon and not buoyant force.