The compressibility of water is 4 x 10⁻⁵ per unit atmospheric pressure. The decrease in volume of 100 cubic centimeter of water under a pressure of 100 atmosphere will be

To find the decrease in volume of water, we can use the definition of compressibility.

Compressibility ($\beta$) is defined as the fractional change in volume per unit change in pressure. Mathematically, it is given by the formula:
$\beta =\frac{\Delta V}{V\times \Delta P}$
where:
- $\beta$ is the compressibility of water,
- $\Delta V$ is the decrease in volume,
- $V$ is the initial volume of water, and
- $\Delta P$ is the change in pressure.

We are given the following values in the problem:
- Compressibility of water, $\beta =4\times {10}^{-5}{\text{atm}}^{-1}$
- Initial volume of water, $V=100{\text{cm}}^3$ (or cc)
- Applied pressure, $\Delta P=100\text{atm}$

Rearranging the formula to solve for the decrease in volume ($\Delta V$):
$\Delta V=\beta \times V\times \Delta P$

Substituting the given values into the equation:
$\Delta V=(4\times {10}^{-5})\times 100\times 100$
$\Delta V=4\times {10}^{-5}\times {10}^4$
$\Delta V=4\times {10}^{-1}$
$\Delta V=0.4\text{cc}$

Therefore, the decrease in volume of the water is 0.4 cc.

The correct option is 0.4 cc.