Q. The compressibility of water is $6 \times 10^{- 10}N^{- 1}m^{2}$. If one litre is subjected to a pressure of $4 \times 10^{7}N\ m^{- 2}$, the decrease in its volume is
A) $2.4\ cc$
B) $10\ cc$
C) $24\ cc$
D) $15\ cc$
Explanation
(c) Bulk modulus, $B = - \frac{P}{\left( \frac{\mathrm{\Delta}V}{V} \right)}$
$-$ve sign shows that with an increase in pressure, a decrease in volume occurs
Compressibility, $k = \frac{1}{B} = - \frac{\mathrm{\Delta}V}{PV}$
Decrease in volume, $\mathrm{\Delta}V = PVk$
$= 4 \times 10^{7} \times 1 \times 6 \times 10^{- 10} = 24 \times 10^{- 3}$ litre
$= 24 \times 10^{- 3} \times 10^{3}cm^{3} = 24\ cc$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.