Question

A ball is falling in a lake of depth $200m$ creates a decrease of $0.1$% in its volume at the bottom. The bulk modulus of the material of the ball will be:

• A. $19.6\times {10}^{-16}$ $N{m}^{-2}$
• B. $19.6\times {10}^8$ $N{m}^{-2}$
• C. $19.6\times {10}^{-8}$ $N{m}^{-2}$
• D. $19.6\times {10}^{16}$ $N{m}^{-2}$

Answer 1

The correct option is C $19.6\times {10}^{-8}$ $N{m}^{-2}$

The density of water is $d={10}^{3}Kg/m^3$

The depth of lake is $h=200m$

The decrease in volume is $0.1$%

The bulk modulus will be $B=V\frac{P}{dV}=\frac{dgh}{\frac{dV}{V}}=\frac{{10}^3\times 9.8\times 200}{{10}^{-3}}=19.6\times {10}^8$