Question

The bulk modulus of water if its volume changes from $100litre$ to $99.5litre$ under a pressure of $100atm$ is $\left(Take1atm=10^{5}N{m}^{-2}\right)$

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

Answer 1

Answer: (C)

According to definition of bulk modulus,
$B=-\frac{p}{\Delta V/V}$
Here, $p=100atm$ $=100\times 10^{5}N$ $m^{-2}$ $=10^{7}N$ $m^{-2}$
$\Delta V$ $=\left(99.5-100\right)litre$ $=-0.5litre$
$v=100litre$
$\therefore$ $B=\frac{10^{7}N{m}^{-2}}{\left(-0.5litre/100litre\right)}$ $=2\times 10^{9}N$ $m^{-2}$