Bulk Modulus & Compressibility

The increase in the pressure required to decrease the volume ( $\Delta V$) of water is $6.3 \times 10^{7}\text{ N/m}^2$. The percentage decrease in the volume is ______.

(Bulk modulus of water $= 2.1 \times 10^{9}\text{ N/m}^2$.)

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text{rd}}$ of its initial volume $(V_{\text{o}} = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5}\text{ N/m}^2$, the magnitude of work done on the gas is ______ J.

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $7 \times 10^{6}\text{ Pa}$, would be __________ $\text{mm}^3$.

(Given bulk modulus of copper $= 1.4 \times 10^{11}\text{ N m}^{-2}$)

The increase in pressure required to decrease the volume of a water sample by $0.2\%$ is $\text{P} \times 10^{5}\text{ Nm}^{-2}$. Bulk modulus of water is $2.15 \times 10^{9}\text{ Nm}^{-2}$. The value of P is _________.

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was _______ litre. (Take 1 atm = 105 Pa)

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$^{-2}$.

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02\%$ is _______ $m$.

(Take density of sea water $= 10^{3}\text{ kgm}^{-3}$, Bulk modulus of rubber $= 9 \times 10^{8}\text{ Nm}^{-2}$, and $g = 10\text{ ms}^{-2}$)

If average depth of an ocean is $4000\text{ m}$ and the bulk modulus of water is $2 \times 10^{9}\text{ Nm}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is _______ (Given, $\text{g} = 10\text{ ms}^{-2},\ \rho = 1000\text{ kg m}^{-3}$)

Under isothermal condition, the pressure of a gas is given by $\text{P} = a\,\text{V}^{-3}$, where $a$ is a constant and $\text{V}$ is the volume of the gas. The bulk modulus at constant temperature is equal to

A certain pressure '$\text{P}$' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is ____________.

The bulk modulus of a liquid is 3 $\times$ 1010 Nm−2. The pressure required to reduce the volume of liquid by 2% is:

An object is located at 2 km beneath the surface of the water. If the fractional compression $\frac{\Delta V}{V}$ is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ____________. [Given: density of water is 1000 kgm−3 and g = 9.8 ms−2]

When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 $\times$ 108 Nm−2, Density of sea water = 103 kgm−3, g = 9.8 m/s2)

The normal density of a material is $\rho$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be:

The compressibility of water is $5 \times 10^{-10}\text{ m}^2\text{/N}$. Pressure of $15 \times 10^{6}\text{ Pa}$ is applied on 100 mL volume of water. The change in the volume of water is

The density of a metal at normal pressure $p$ is $\rho$. When it is subjected to an excess pressure, the density becomes $\rho'$. If $K$ is the bulk modulus of the metal, then the ratio $\frac{\rho'}{\rho}$ is

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to:

(Given bulk modulus of metal, B = 8 $\times$ 1010 Pa)

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left(\frac{dr}{r}\right)$ is:

The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'P', the fractional decrease in radius is

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $\Delta$a) where ($\Delta$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $\mu$ then the force needed to push the cork into the bottle is:

The approximate depth of an ocean is 2700 m. The compressiblity of water is 45.4 $\times$ 10−11 Pa−1 and density of water is 103 kg/m3. What fractional compression of water will be obtained at the bottom of the ocean?

The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25 and 2.2 respectively in units of 109 Nm−2. For a given value of pressure, the fractional compression in volume is $\frac{\Delta V}{V}$. Which of the following statements about $\frac{\Delta V}{V}$ for these three liquids is correct?