Question

A sphere contracts in volume by $0.01$% when taken to the bottom of lake $1km$ deep. If the density of water is $1gm/cc$, the bulk modulus of water is

• A. 9.8 x 10${}^5$N/m${}^2$
• B. 9.8 x 10${}^8$N/m${}^2$
• C. 9.8 x 10${}^{10}$N/m${}^2$
• D. 9.8 x 10${}^6$N/m${}^2$

Answer 1

The correct option is C 9.8 x 10${}^{10}$N/m${}^2$

$B=\frac{\Delta p}{\Delta v/v}=\frac{\rho g\Delta h}{\Delta v/v}$
$=\frac{1000\times 9.8\times 1000}{0.00\times {10}^{-2}}$
Bulk Modulus $=9.8\times {10}^{10}N/m^2$