Question

Bulk modulus for rubber is $9.8\times {10}^5{\text{N/m}}^2.$ To what depth should a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$?

• A. $10\text{m}$
• B. $100\text{m}$
• C. $200\text{m}$
• D. $20\text{m}$

Answer 1

The correct option is B $100\text{m}$

Let $B$ represent bulk modulus, then

$B=-\frac{\left(\Delta P\right)V}{\Delta V}$

$\Rightarrow \Delta P=-\frac{B\Delta V}{V}$

Let $h$ be the required depth and the density of water be $\rho .$

Then

$h\rho g=-B\frac{\Delta V}{V}$

$h=-\frac{B\Delta V}{\rho gV}$

$\therefore h=\frac{9.8\times {10}^8\times (-0.1)}{{10}^3\times 9.8\times 100}=100\text{m}$

Hence, option $\left(\text{B}\right)$ is correct.