Question

A spherical ball contracts in volume by $0.02\%$ when subjected to a pressure of $100$ atmosphere. Assuming one atmosphere $={10}^{8}N{m}^{-2}$, the bulk modulus of the material of the ball is

• A. $0.02\times {10}^{5}N/m^2$
• B. $0.02\times {10}^{7}N/m^2$
• C. $50\times {10}^{7}N/m^2$
• D. $50\times {10}^{9}N/m^2$

Answer 1

The correct option is D $50\times {10}^{9}N/m^2$

$B=-V\frac{dP}{dV}$
Given $dP=100atm,\frac{dV}{V}=-0.0002$
Thus, $B=-\frac{100}{-0.0002}=5\times {10}^5$ in atm units.
$1atm={10}^{5}Pa$, thus in SI units, $B=5\times {10}^{10}=50\times {10}^{9}N/m^2$