Question

A rubber ball is taken to depth $1$ km inside water so that its volume reduces by $0.05\%$.What is the bulk modulus of the rubber:

• A. $2\times {10}^{10}N/m^2$
• B. $2\times {10}^{9}N/m^2$
• C. $2\times {10}^{7}N/m^2$
• D. $2\times {10}^{11}N/m^2$

Answer 1

The correct option is A $2\times {10}^{10}N/m^2$

Pressure at $1km$ depth inside water,
$P=1000\times 10\times 1000={10}^{7}N{m}^{{}_2}$
say, V=volume of ball
$\frac{0.05}{100}\times V$ = Reduction in volume (i.e) $\Delta V$
Bulk Modulus, $\beta =\frac{-PV}{\Delta V}=\frac{-{10}^7\times V}{\frac{-0.05V}{100}}$

$=2\times {10}^{10}N{m}^{-2}$

Hence Option $\text{A}$ is correct.