Question

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. ( The bulk modulus of rubber is $9.8\times {10}^8$ $N/m^2$ ; and the density of sea water is ${10}^3$ $kg/m^3$)

• A. 0.1 m
• B. 1 m
• C. 10 m
• D. 100 m

Answer 1

The correct option is D 100 m

Bulk modules of rubber $\left(B\right)=9.8\times {10}^{8}N/m^2$

Density of sea water $\left(\rho \right)={10}^{3}kg/m^3$

Percentage decreases in volume $,$

$(\Delta V/V\times 100)=0.1or\Delta V/V=0.1/100$

OR $,\Delta V/V=1/1000$

Let the rubber ball be taken up to depth $h.$

$\because$ Change in pressure$\left(p\right)=h\rho g$

$\therefore$ Bulk modules $\left(B\right)=p/\left(\Delta V/V\right)=h\rho g/\left(\Delta V/V\right)$

OR $,h=B\times \left(\Delta V/V\right)/\rho g=9.8\times {10}^8\times 1/1000/{10}^3\times 9.8=100m$

Hence,

option $\left(D\right)$ is correct answer.