Compressibility

Q. The approximate depth of an ocean is $2700\text{m}$. The compressibility of water is $45.4\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. Fractional compression of water will be:
[Take $g=10{\text{m/s}}^2$]

1. $0.8\times {10}^{-2}$
2. $1.0\times {10}^{-2}$
3. $1.2\times {10}^{-2}$
4. $1.4\times {10}^{-2}$

Q. The compressibility of water is $5\times {10}^{-10}{\text{m}}^2\text{/N}$. If it is subjected to a pressure of $15\text{MPa}$, the fractional decrease in volume will be:

1. $3.3\times {10}^{-5}$
2. $7.5\times {10}^{-3}$
3. $1.5\times {10}^{-2}$
4. $5.6\times {10}^{-4}$

Q. A solid copper cube of edge $10\text{cm}$ is subjected to a hydraulic pressure of $7\times {10}^6\text{Pa}$. If compressibility of copper is $\frac{1}{140}{\text{GPa}}^{-1}$, then contraction in its volume will be

1. $2\times {10}^{-8}{\text{m}}^3$
2. $5\times {10}^{-8}{\text{m}}^3$
3. $4\times {10}^{-8}{\text{m}}^3$
4. ${10}^8{\text{m}}^3$

Q.

The compressibility of a material is

1. None of the above

2. Product of volume and its pressure

3. The fractional change in volume per unit change in pressure

4. The change in pressure per unit change in volume strain

Q.

Water is filled in a conical flask up to height $20cm$. If the radius of base is $10cm$ and the atmospheric pressure is $1.01\times {10}^{5}Pa$. Find the force exerted on bottom of the flask?

Q. The approximate depth of an ocean is $3500\text{m}$. The compressibility of water is $50\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. Find the fractional compression of water that will be obtained at the bottom of the ocean. (Take $g=10{\text{m/s}}^2$)

1. $5.25\times {10}^{-2}$
2. $1.75\times {10}^{-2}$
3. $10.5\times {10}^{-2}$
4. $2.625\times {10}^{-2}$

Q.

If $500\mathrm{ml}$of a gas A at $1000$ torr and $1000\mathrm{ml}$ of gas B at $800$ torr are placed in $2\mathrm{L}$ a container, the final pressure will be

Q. The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = 13.6, Density of water $={10}^{3}kg/m^3,g=9.8m/s^2$ at Calcutta$.Pressure=hpg$ in usual symbols.

Q.

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is

1. 10m

2. 5m

3. 15m

4. 20m

Q. The compressibility of water is $4\times {10}^{-5}$ per unit atmospheric pressure. The decrease in volume of $100c{m}^3$ of water under a pressure of 100 atmosphere will be

1. $0.4c{m}^3$
2. $0.4\times {10}^{-5}c{m}^3$
3. $0.04c{m}^3$
4. $0.025c{m}^3$

Q. A solid copper cube of edge $10\text{cm}$ is subjected to a hydraulic pressure of $7\times {10}^6\text{Pa}$. If compressibility of copper is $\frac{1}{140}{\text{GPa}}^{-1}$, then contraction in its volume will be

1. $5\times {10}^{-8}{\text{m}}^3$
2. $4\times {10}^{-8}{\text{m}}^3$
3. $2\times {10}^{-8}{\text{m}}^3$
4. ${10}^8{\text{m}}^3$

Q.

What is the unit of compressibility?

Q. The initial volume of water is $2000{\text{cm}}^3$. Determine the change in volume of the water when external pressure is changed from ${10}^5{\text{Nm}}^{-2}$ to ${10}^6{\text{Nm}}^{-2}$.
[Take compressibility of water as $60\times {10}^{-11}{\text{m}}^2/\text{N}$]

1. $2.08\times {10}^{-5}{\text{m}}^3$
2. $1.08\times {10}^{-6}{\text{m}}^3$
3. $2.08\times {10}^{-6}{\text{m}}^3$
4. $1.08\times {10}^{-5}{\text{m}}^3$

Q.

A solid sphere of radius R and made of a material of bulk modulus K is completely immersed in a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, $\frac{\delta R}{R}$ is given by

1. $\frac{Mg}{KA}$

2. $\frac{Mg}{2KA}$

3. $\frac{Mg}{3KA}$

4. $\frac{Mg}{4KA}$

Q. The density of a metal at normal pressure is $\rho$. It's density when it is subjected to an excess pressure p is $\rho$'. If B is the bulk modulus of the metal, the ratio $\rho$'/$\rho$ is :

1. $\frac{1}{1-p/B}$
2. $1+\frac{P}{B}$
3. $\frac{1}{1-B/p}$
4. $1+B/p$

Q. Bulk modulus for rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth should a rubber ball be taken in a lake, so that its volume is decreased by $0.1$%?

1. $10\text{m}$
2. $100\text{m}$
3. $200\text{m}$
4. $20\text{m}$

Q. For a saturated sand deposit, the porosity and the specific gravity of solids are 40% and 2.7 respectively. The critical hydraulic gradient at which boiling starts is:

1. 0.98
2. 1.02
3. 1.08
4. 1.21

Q. A cube at temperature $0^{o}C$ is compressed equally from all sides by an external pressure $P$. By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied. The bulk modulus of the material of the cube is $B$ and the coefficient of linear expansion is $\alpha$.

1. $P/B\alpha$
2. $3\pi \alpha /B$
3. $P/3B\alpha$
4. $3B/P$

Q. A wide vessel with a small hole in the bottom is filled with water and kerosene. Neglecting the viscosity, find the velocity of the water flow, if the thickness of the water layer is equal to $h_1=30cm$ and that of the kerosene layer to $h_2=20cm$.Density of kerosene $=600\mathrm{kg}/m^3$

1. $3.82{ms}^{-1}$
2. $5.74{ms}^{-1}$
3. $1.91{ms}^{-1}$
4. $2.87{ms}^{-1}$

Q. A steel wire of length $l=1\text{m}$ and of circular cross-section $1\text{mm}$ is under tension $F$. The extension is $x$. If it is recast into a wire of square cross-section of side $1\text{mm}$ under same tension, it has extension ${\pi }^{n}x$. Where $n=$

Q.

A solid sphere of radius R and made of a material of bulk modulus K is completely immersed in a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, $\frac{\delta R}{R}$ is given by

1. $\frac{Mg}{KA}$

2. $\frac{Mg}{2KA}$

3. $\frac{Mg}{3KA}$

4. $\frac{Mg}{4KA}$

Q. Compressibility of water is $5\times {10}^{-10}{m}^2/N.$ Find the decrease in volume of 100 mL of water when subjected to a pressure of 15 MPa.

1. $=-0.95mL$
   
2. $=-0.85mL$
   
3. $=-0.75mL$
   
4. $=-0.65mL$
   

Q. The average depth of Indian ocean is about 3000 m Bulk Modulus of water is $2.2\times {10}^{4}N/m^2$ , $g=10m/s^2$, then the fractional compression is $\frac{\Delta V}{V}$ of water at the bottom of Indian Ocean is:

1. $12.6$ %
2. $20.6$ %
3. $0.52$ %
4. $13.6$ %

Q. A thin square plate of side, $l=10cm$ is dragged with constant velocity, $v$ = $3$ $cm/s$ in an oil. The width $d$ of the oil column is $2mm$. Square plate is placed symmetrically as shown in the figure. Assumed velocity of layer of oil at the end is negligible. The coefficient of viscosity is $150$ $poise$. Find the horizontal force (in $N$) required to move the square plate with constant velocity.

Q. The property of fluid which enables it to resist tensile stress is known as

1. compressibility
2. cohesion
3. adhesion
4. surface tension

Q. A wire of length $1m$ and radius $1mm$ is subjected to a load. The extension is $x$. The wire is melted and then drawn into a wire of square cross-section of side $1mm$. What is the extension under the same load?

1. ${\pi }^{2}x$
2. $\pi x^2$
3. $\pi x$
4. $\pi /x$

Q. A cube is subjected to a uniform volume compression. If the side of the cube decreases by
2$\%$ , the bulk strain is:

1. $0.02$
2. $0.03$
3. $0.04$
4. $0.06$

Q. A ball of density ${\rho }_b$ falls from rest from a point P on to the surface of a liquid of density ${\rho }_l$ in time T. It falls, enters the liquid, stops, moves up and returns to P in a total time 3T. Neglect viscosity, surface tension and splashing. The ratio $\frac{{\rho }_l}{{\rho }_b}$ will be equal to:

1. 1
2. 3
3. 2
4. 9

Q.

Unit for pressure used in weather maps is millibar. 1 millibar is equal to

1. 1000 bar
2. 100 Pa
3. 100 kPa
4. 1 atm

Q.

The density of water at the surface of the ocean is $\rho$. If the bulk modulus of water is B, what is the density of ocean water at a depth where the pressure is $n{P}_0$, where $P_0$ is the atmospheric pressure?

1. $\frac{\rho B}{B-(n-1)P_0}$

2. $\frac{\rho B}{B+(n-1)P_0}$

3. $\frac{\rho B}{B-n{P}_0}$

4. $\frac{\rho B}{B+n{P}_0}$