Compressibility

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

1. 0.025 cc

2. 0.004 cc

3. 0.4 cc

4. 

Q.

What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is $1.03\times {10}^{3}kg/m^3$?

Q. In a test experiment on a model airplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70m{s}^{-1}$ and $63m{s}^{-1}$ respectively. What is the lift on the wing if its area is $2.5$ m${}^2$ ? Take the density of air to be $1.3kg{m}^{-3}$.

Q.

Find the decrease in the volume of a sample of water from the following data. Initial volume = 1000 cm³, initial pressure = 10⁵ N m^-2, final pressure = 10⁶ N m^-2, compressibility of water = 50 x 10^-11 m² N^-1.

1. 0.90 c

2. 0.25

3. 0.50

4. 0.45

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

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

Q.

Find the decrease in the volume of a sample of water from the following data. Initial volume = 1000 cm³, initial pressure = 10⁵ N m^-2, final pressure = 10⁶ N m^-2, compressibility of water = 50 x 10^-11 m² N^-1.

1. 0.90 c$m^4$

2. 0.45 $c{m}^3$

3. 0.25 $c{m}^3$

4. 0.50 $c{m}^3$

Q.

The compressibility of a material is

1. Product of volume and its pressure

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

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

4. None of the above

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. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50, 000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

Q. A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at ${250}^{o}C$, if the original lengths are at ${40.0}^{o}C$? Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass $=2.0\times {10}^{-5}{K}^{-1}$, steel $=1.2\times {10}^{-5}{K}^{-1})$

Q. A stone of mass $0.25kg$ tied to the end of a string is whirled round in a circle of radius $1.5m$ with a speed of $40rev./min$ in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of $200N$?

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

Q. A stream of water flowing horizontally with a speed of $15$ $m{s}^{-1}$ gushes out of a tube of cross-sectional area ${10}^{-2}$ $m^2$, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound ?

Q.

The value of surface tension of a liquid at critical temperature is

1. Infinite

2. Zero

3. Between 0 and ∞

4. Can not be determined