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EEJ MAIN Physics QUESTION #7083
Question 1
A solid sphere (radius $r$, bulk modulus $K$) is in a liquid. A mass $m$ is placed on a piston of area $a$ to compress the liquid. Find the fractional decrease in radius $\frac{dr}{r}$.
  • $\frac{mg}{3Ka}$✔️
  • $\frac{mg}{Ka}$
  • $\frac{Ka}{mg}$
  • $\frac{3Ka}{mg}$
Correct Answer Explanation

Bulk Modulus $K = \frac{\Delta P}{-\Delta V/V}$.

  • The change in pressure is $\Delta P = \frac{mg}{a}$.
  • The fractional change in volume for a sphere is $\frac{\Delta V}{V} = 3\frac{dr}{r}$.
  • $K = \frac{mg/a}{3dr/r} \implies \frac{dr}{r} = \frac{mg}{3Ka}$.