Question

A rubber ball is taken to a 100 m deep lake and its volume changes by $0.1\%$ . The bulk modulus rubber is nearly-

• A. $1\times {10}^{6}N/m^2$
• B. $1\times {10}^{8}N/m^2$
• C. $1\times {10}^{7}N/m^2$
• D. $1\times {10}^{9}N/m^2$

Answer 1

The correct option is D $1\times {10}^{9}N/m^2$

$\begin{array}{c}\text{given Depth}=100m\\ \text{Percentage change in volume}=\frac{\Delta V}{V}\times 100=0.1\%\\ \text{let}h\text{be depth \&}\rho \text{be density of water}\\ \text{Pressure at a depth}h=h\rho g\\ P=\left(100\right)\times \left(1000\right)\times \left(10\right)\end{array}$

$\begin{array}{cc}\text{Bulk modulus}& =\frac{p}{\frac{dv}{v}}\\ B=& \frac{100\times {10}^3\times 10}{\left(\frac{0.1}{100}\right)}\\ & =\frac{100\times {10}^3\times 10}{{10}^{-3}}\\ B& =1\times {10}^{9}N/m^2\end{array}$