Question

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by $0.1\%$.
(Take, density of sea water =$10^{3}kg$ $m^{-3}$, bulk modulus of rubber =$9\times 10^{8}N$ $m^{-2}$, $g=10m$ $s^{-2})$

• A. $9m$
• B. $18m$
• C. $90m$
• D. $180m$

Answer 1

Answer: (C)

Let $h$ be the depth at which the rubber ball is taken. Then
$p=h\rho g\dots \left(i\right)$
By definition of bulk modulus,
$B=-\frac{P}{\Delta V/V}$
The negative sign shows that with increase in pressure, a decrease in volume occurs.
$\therefore$ $P=B\frac{\Delta V}{V}$
Using $\left(i\right)$,
$h\rho g$=$B\frac{\Delta V}{V}$ or $h=\frac{B}{\rho g}$ $\frac{\Delta V}{V}$
Substituting the given values, we get
$h=\frac{9\times 10^{8}N{m}^{-2}}{10^{3}kg{m}^{-3}\times 10m{s}^{-2}}$ $\left(\frac{0.1}{100}\right)$ $=90m$