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A soild sphere is initially kept in open air, and the pressure exerted on it by air is 1.0×105N/m2 (atmospheric pressure). The sphere is lowered into the ocean to a depth where the pressure is 200 times the atmospheric pressure. The volume of the sphere in air is 0.5m3. What is the change in the volume once the sphere is submerged ? Given that bulk modulus is 6.1×1010N/m2.

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What happens when you squeeze a tennis ball in your hand ? Its volume reduces as it shrinks. We can expect same to happen to the sphere when it is subjected to high pressure from the ocean water. We need to perform a simple calculation using Eq. 12-5.
ΔU=V,ΔpB.
Substituting the numerical values :
ΔV=(0.50m3)(2.0×107N/m21.0×105N/m2)6.1×1010N/m2
=1.6×104/m3.
The negative sign indicates that the volume of the sphere decreases when submerged.

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Updated on:21/07/2023

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