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A solid sphere of radius R and bulk modulus K is immersed in a liquid held in a cylindrical vessel. A massless piston of area A rests on the liquid surface. When a mass m is placed on the piston, compressing the liquid, what is the fractional change in the sphere's radius, dR/R?
- mg/(AK)
- mg/(3AK)
- mg/A
- mg/(3AR)
Correct answer: mg/(3AK)
Solution
The pressure increase mg/A compresses the sphere; since dV/V = dP/K and dR/R = (1/3) dV/V, the radius decreases by mg/(3AK).
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