Question

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

• 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

The correct option is C $2\times {10}^{9}N{m}^{-2}$

Given:
Here, $P=100atm=100\times {10}^{5}N{m}^{-2}={10}^{7}N{m}^{-2};\Delta V=(99.5-100)litre=-0.5litre;V=100litres$

According to the definition of bulk modulus,

$B=-\frac{P}{\Delta V/V}$

$\therefore B=-\frac{{10}^{7}N{m}^{-2}}{(-0.5/100litre)}=2\times {10}^{9}N{m}^{-2}$