Question

A rubber ball is brought into 200 m deep water, its volume is decreased by 0.1% then volume elasticity coefficient of the material of ball will be:
$(Given\rho ={10}^{3}kg/m^3$ and $g=9.8m{s}^{-2})$

• A. $19.6\times {10}^{8}N/m^2$
• B. $19.6\times {10}^{-10}N/m^2$
• C. $19.6\times {10}^{10}N/m^2$
• D. $19.6\times {10}^{-8}N/m^2$

Answer 1

The correct option is A $19.6\times {10}^{8}N/m^2$

According to bulk modulus of elasticity,
$B=-\frac{\Delta P}{\Delta V/V}$

According to pressure depth relation,
$P=h\rho g$

$B=-\frac{h\rho g}{\Delta V/V}$

or, $B=\frac{200\times {10}^3\times 9.8}{\frac{1}{1000}}$

or, $B=19.6\times {10}^{8}N/m^2$