Compressibility

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

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

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

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.

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

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

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

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. 0.4 cc
2. 0.025 cc
3. 0.004 cc
4. 4 X 10^-5 cc

Q.

The compressibility of a material is

1. Product of volume and its pressure

2. None of the above

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

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

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. 0.45

2. 0.50

3. 0.25

4. 0.90 c