Question

The bulk modulus of rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth a rubber ball must be taken in a lake so that its volume is decreased by $0.1\%$?
(Neglect atmospheric pressure)

• A. $25\text{m}$
• B. $100\text{m}$
• C. $200\text{m}$
• D. $500\text{m}$

Answer 1

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

We know,
Bulk modulus, $K=\frac{P}{\Delta V/V}$
or $P=K\frac{\Delta V}{V}$
$\therefore P=9.8\times {10}^8\times \left(\frac{0.1}{100}\right)$
At depth $h$, $P=\rho gh$
$\Rightarrow h\rho g=9.8\times {10}^8\times \left(\frac{0.1}{100}\right)$
$\therefore h=\frac{9.8\times {10}^8}{1000\times 9.8}\times \frac{0.1}{100}\text{m}=100\text{m}$