Question

The pressure increases by 1.0 x 104 N/m2 for every meter of depth beneath the surface of the ocean. At what depth does the volume of a Pyrex (bulk modulus 2.6 x 1010 N/m2) glass cube, 5.4 x 10-2 m on an edge at the ocean's surface, decrease by 6.0 x 10-10 m3

Answer 1

Given that,

Bulk modulus $B= 2.6\times10^{10}\ N/m^2$

Change in volume $\Delta V=6.0\times10^{-10}\ m^3$

Edge $a= 5.4\times10^{-2}\ m$

The volume of the cube at the ocean's surface will be

$V_{0}=a^3$

Where, a = edge

Put the value into the formula

$V_{0}=(5.4\times10^{-2})^3$

$V_{0}=0.00016\ m^3$

We need to calculate the change in pressure

Using formula of pressure

$\Delta P=-B\dfrac{\Delta V}{V_{0}}$

Put the value into the formula

$\Delta P=-(2.6\times10^{10})\times\dfrac{(-6.0\times10^{-10})}{0.00016}$

$\Delta P=97500\ N/m^2$

The pressure increases by $1.0\times 10^{4}\ N/m^2$ for every meter of depth

We need to calculate the depth

Using formula for depth

$depth=\dfrac{97500}{1.0\times10^{4}}$

$depth=9.75\ m$

Hence,  The depth is 9.75 m.