Question

When a sphere is taken to bottom of sea 1 km deep, it contracts by 0.01%. The bulk modulus of elasticity of the material of sphere is (Given, density of water $= 1 gcm^{-3})$

• A. $9.8\times10^{10}Nm^{-2}$
• B. $10.2\times10^{10}Nm^{-2}$
• C. $0.98\times10^{10}Nm^{-2}$
• D. $8.4\times10^{10}Nm^{-2}$

Answer 1

Answer: (A)

Bulk modulus $B=\frac{\Delta p}{\frac{-\Delta V}{V}}$
$\frac{-\Delta V}{V}=\frac{0.01}{100}=10^{-4}$
$\Delta p=pressure of water=h\rho g$
= $10^3\times1\times10^\times9.8$
$\Delta p=9.8\times10^6$
$B=\frac{9.8\times10^6}{10^{-4}}$
$=9.8\times10^{10}Nm^{-2}$