Question

Bulk modulus for rubber is $9.8 \times 10^{8} Nm ^{-2}$. To what depth (in $m$ ) should a rubber ball be taken in a lake so that its volume is decreased by $0.1 \%$ ?

Answer 1

$K=\frac{(\Delta P) V}{\Delta V} \text { or } \Delta P=\frac{K \Delta V}{V}$
Let $h$ be the required depth and the density of water be $\rho$.
Then $h \rho g=\frac{K \Delta V}{V}$
or $h=\frac{K \Delta V}{\rho g V}=\frac{9.8 \times 10^{8} \times 0.1}{10^{3} \times 9.8 \times 100}$
$=100\, m$