Question

The bulk modulus of water if its volume changes from $100\, litre$ to $99.5\, litre$ under a pressure of $100 \,atm$ is $\left(Take 1 \,atm =10^{5 }N m^{-2}\right)$

• A. $2\times10^{7} N$ $m^{-2}$
• B. $2\times10^{8} N$ $m^{-2}$
• C. $2\times10^{9} N$ $m^{-2}$
• D. $2\times10^{10} N$ $m^{-2}$

Answer 1

Answer: (C)

According to definition of bulk modulus,
$B=-\frac{p}{\Delta V/ V}$
Here, $p=100 \,atm $ $=100\times10^{5}N$ $m^{-2}$ $=10^{7}N$ $m^{-2}$
$\Delta V$ $=\left(99.5-100\right)litre$ $=-0.5 \, litre$
$v=100 \, litre$
$\therefore \quad$ $B=\frac{10^{7}N m^{-2}}{\left(-0.5 \,litre /100 \,litre\right)}$ $=2\times10^{9} N$ $m^{-2}$