Question

A ball falling-in a lake of depth 400 m has a decrease of $0.2\%$ in its volume at the bottom. The bulk modulus of the material of the ball is (in $N{m}^{-}2$)

• A. $9.8\times {10}^9$
• B. $9.8\times {10}^{10}$
• C. $1.96\times {10}^{10}$
• D. $9.8\times {10}^{11}$
• E. $1.96\times {10}^9$

Answer 1

The correct option is E $1.96\times {10}^9$

Given, $h=400m,\frac{△V}{V}=\frac{0.2}{100}$
We know that the bulk modulus of the material
$B=\frac{hpg}{\left(\begin{array}{c}\frac{△V}{V}\end{array}\right)}$
$B=\frac{400\times {10}^3\times 9.8}{\frac{0.2}{100}}$
$B=\frac{400\times {10}^3\times 9.8\times 100}{0.2}$
$B=2000\times {10}^3\times 9.8\times 100$
$B=1.96\times {10}^{9}N{m}^{-2}$