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)

$90m$

Let $h$ be the depth at which the rubber ball be taken, Then
$P=h\rho g...\left(i\right)$
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 (i)
$h\rho g=B\frac{\Delta V}{V}orh=\frac{B}{\rho g}\frac{\Delta V}{V}$
Substituting the given values, we get
$h=\left(\frac{9\times {10}^{8}N{m}^{-2}}{{10}^{3}kg{m}^{-3}\times {10}^{}m{s}^{-2}}\right)\left(\frac{0.1}{100}\right)=90m$