Question

A ball falling in a lake of depth $200m$ shows a decrease of $0.1\%$ in its volume at the bottom. The bulk modulus of the elasticity of the material of the ball is (take $g=10m/s^2)$.

• A. ${10}^{9}N/m^2$
• B. $2\times {10}^{9}N/m^2$
• C. $3\times {10}^{9}N/m^2$
• D. $4\times {10}^{9}N/m^2$

Answer 1

Answer: (B)

$2\times {10}^{9}N/m^2$

Bulk Modulus is given by;

$B=-V\frac{dP}{dV}$
Now, change in pressure, $dP=\rho gh=1000\times 10\times 200=2\times {10}^6$
Also, given $\frac{dV}{V}=-0.001$
Thus, $B=-\frac{2\times {10}^6}{-0.001}=2\times {10}^9$