Question

The bulk modulus of rubber is$9.1\times {10}^{8}N/m^2$ .To what depth (approximately) a rubber ball betaken in a lake so that its volume is decreased by0.1$\%$?

• A. 25$m$
• B. 100$m$
• C. 200$m$
• D. 500$m$

Answer 1

The correct option is B 100$m$

Given. Bulk modulues $\left(\beta \right)=9.1\times {10}^{8}N/m^2$

$\left|\frac{\Delta V}{V}\right|=0.1\%$ let it is taken at a be depth of h. $dP=Pgh$

$\begin{array}{c}\text{We know,}\\ B=-\frac{dP}{\frac{dV}{V}}=\frac{Pgh}{{10}^{-3}}=9.1\times {10}^8\end{array}$

$h=\frac{9.1\times {10}^5}{{10}^3\times 19.8}=\simeq \text{l0om.}$