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EEJ MAIN Physics QUESTION #7101
Question 1
A soft sphere of radius $r$ and bulk modulus $K$ is in a liquid. If a mass $m$ is placed on a piston of area $a$ to compress the liquid, find the fractional decrease in radius ($\frac{dr}{r}$) [cite: 461, 462, 463, 465].
  • $\frac{mg}{3Ka}$✔️
  • $\frac{mg}{Ka}$
  • $\frac{Ka}{mg}$
  • $\frac{3Ka}{mg}$
Correct Answer Explanation

Bulk modulus is $K = \frac{\Delta P}{\Delta V / V}$ [cite: 461].

  • $\Delta P = \frac{mg}{a}$ (pressure from piston) [cite: 462, 463]
  • For a sphere, $V = \frac{4}{3}\pi r^3 \implies \frac{\Delta V}{V} = 3\frac{dr}{r}$
  • $K = \frac{mg/a}{3dr/r} \implies \frac{dr}{r} = \frac{mg}{3Ka}$[cite: 466].