Question 26: Properties of Matter

Question

The fractional compression $\left( \frac{\Delta V}{V} ight)$ of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = $2 	imes 10^9$ N m$^{-2}$, density of water = $10^3$ kg m$^{-3}$, acceleration due to gravity $g = 10$ m s$^{-2}$.

Accepted Answer

The fractional compression $\left( \frac{\Delta V}{V} ight)$ of water at a depth of 2.5 km below sea level is calculated as follows:
Given:
Bulk modulus of water, $B = 2 	imes 10^9 \, 	ext{N/m}^2$
Density of water, $ho = 10^3 \, 	ext{kg/m}^3$
Acceleration due to gravity, $g = 10 \, 	ext{m/s}^2$
The relationship between pressure change and volume change using the bulk modulus is given by:
$ B = \frac{ho gh}{\left(\frac{\Delta V}{V}ight)} $
Rearranging the formula to solve for the fractional compression:
$ \frac{\Delta V}{V} 	imes 100 = \frac{ho gh}{B} 	imes 100 $
Substituting in the given values:
$ \frac{1000 	imes 10 	imes 2.5 	imes 10^3}{2 	imes 10^9} 	imes 100\% $
Calculating the result gives:
$ = 1.25\% $
Thus, the fractional compression of water at this depth is 1.25%.

Answer

1.0

Answer

1.25

Answer

1.75

Answer

1.5

Properties of Matter

The fractional compression \left( \frac{\Delta V}{V} \right) of water at the depth of 2.5 km below the sea level is __________ %. Given, the Bulk modulus of water = 2 \times 10^9 N m^{-2}, density of water = 10^3 kg m^{-3}, acceleration due to gravity g = 10 m s^{-2}.

Choose the correct answer: