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A solid sphere of radius r made of a material with bulk modulus K is surrounded by liquid in a cylindrical container. A massless piston of cross-sectional area a covers the entire liquid surface. When a mass m is placed on the piston, what is the fractional decrease in the radius of the sphere, |dr/r|?
- Ka/3mg
- mg/3Ka
- mg/Ka
- Ka/mg
Correct answer: mg/3Ka
Solution
dP = mg/a. dV/V = dP/K = mg/(Ka). Since dV/V = 3*|dr/r|, we get |dr/r| = mg/(3Ka).
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