Bulk Modulus

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

1. $\frac{P}{B}$
2. $\frac{B}{3P}$
3. $\frac{3P}{B}$
4. $\frac{P}{3B}$

Q. The average depth of Indian Ocean is about $3000\text{m}$. The fractional compression, $\frac{\Delta V}{V}$of water at the bottom of the ocean (given that the bulk modulus of the water =$2.2\times {10}^9{\text{Nm}}^{-2}{\text{and g=10 ms}}^{-2}$, assuming density of water remains constant) is

1. $0.82\%$
2. $0.91\%$
3. $1.36\%$
4. $1.52\%$

Q. A spherical ball contracts in volume by $0.02\%$ when subjected to a normal uniform pressure of $100\text{atm}$. The bulk modulus of its material is

1. $2.02\times {10}^{10}{\text{N/m}}^2$
2. $1.01\times {10}^{11}{\text{N/m}}^2$
3. $5.05\times {10}^{10}{\text{N/m}}^2$
4. $1.01\times {10}^{10}{\text{N/m}}^2$

Q.

What is the Young's modulus for a perfect rigid body?

Q. A solid sphere of radius $R$ made of a material of bulk modulus $B$ is surrounded by a liquid in a cylindrical container. A massless piston of area $A$ floats on the surface of the liquid. Find the fractional decrease in the radius of the sphere $\left(\frac{\Delta R}{R}\right)$, when a mass $M$ is placed on the piston to compress the liquid.

1. $\frac{Mg}{AB}$
2. $\frac{Mg}{2AB}$
3. $\frac{Mg}{4AB}$
4. $\frac{Mg}{3AB}$

Q. The pressure of a medium is changed from $1.01\times {10}^5$ Pa to $1.165\times {10}^5$ Pa and change in volume is 10% keeping temperature constant. The bulk modulus of the medium is

1. 204.8 X 10⁵ Pa
2. 51.2 X 10⁵ Pa
3. 1.55 X 10⁵Pa
4. 102.4 X 10⁵ Pa

Q.

The SI unit of compressibility is

1. $m^2/N$

2. $N{m}^2$

3. $N/m^2$

4. $kg/m^3$

Q. What are the applications of elasticity?

Q. The bulk modulus of rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth a rubber ball must be taken in a lake so that its volume is decreased by $0.1\%$?
(Neglect atmospheric pressure)

1. $25\text{m}$
2. $100\text{m}$
3. $200\text{m}$
4. $500\text{m}$

Q. A copper ball of mass $100gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100gm$, filled with $170gm$ of water at room temperature. Subsequently, the temperature of the system is found to be ${75}^{o}C$. $T$ is equal to
(Given : Room temperature $={30}^{o}C$, specific heat of copper $=0.1cal/g{m}^{o}C$)

1. ${825}^{o}C$
2. ${800}^{o}C$
3. ${885}^{o}C$
4. ${1250}^{o}C$

Q.

What is the best definition of elasticity?

Q.

If $Y$, $K$ and $\eta$ are the values of Young’s modulus, bulk modulus, and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

1. $K=\frac{Y\eta }{9\eta -3Y}N/m^2$

2. $\eta =\frac{3KY}{9K+Y}$

3. $Y=\frac{9K\eta }{3K-\eta }$

4. $Y=\frac{9K\eta }{2\eta +3K}$

Q.

The isothermal elasticity of a gas is equal to

1. Density

2. Volume

3. Pressure

4. Specific heat

Q. When two liquid of same mass but different density do and do are mixed together, then density of mixture is

Q.

Why is Youngs Modulus important?

Q. What is the value of bulk modulus for an incompressible liquid?

1. zero
2. infinite
3. one
4. some random value

Q. When pressure of a gas (at ${20}^{\circ }\text{C}$ temperature) is changed from $P_1=1.01\times {10}^5\text{Pa}$ to $P_2=1.165\times {10}^5\text{Pa}$, the volume changes by $10$%. Then the bulk modulus of the gas is

1. $1.4\times {10}^5\text{Pa}$
2. $1.55\times {10}^5\text{Pa}$
3. $0.155\times {10}^5\text{Pa}$
4. $1.01\times {10}^5\text{Pa}$

Q.

The height of mercury which exerts the same pressure as $20\mathrm{cm}$ of water column, is equal to

1. $1.48\mathrm{cm}$

2. $14.8\mathrm{cm}$

3. $148\mathrm{cm}$

4. None of these

Q. For a constant volumetric stress on an object, the fractional change in the object volume $\left(\frac{\Delta V}{V}\right)$ and its bulk modulus $\left(B\right)$ are related as

1. $\frac{\Delta V}{V}\propto B$
2. $\frac{\Delta V}{V}\propto \frac{1}{B}$
3. $\frac{\Delta V}{V}\propto B^2$
4. $\frac{\Delta V}{V}\propto B^{-2}$

Q. Fractional change in the radius of a sphere of bulks modulus $B$, when it is compressed by pressure $P$ from all sides is

1. $\frac{4P}{3B}$
2. $\frac{3P}{B}$
3. $\frac{P}{B}$
4. $\frac{P}{3B}$

Q. The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume?
(The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$)

1. $\frac{P\beta }{\alpha }$
2. $\frac{P}{\alpha \beta }$
3. $\frac{P\alpha }{\beta }$
4. $\frac{\alpha \beta }{P}$

Q. When a rubber ball is taken to the bottom of a sea of depth $2000\text{m}$, the volume of the rubber ball decreases by $1.5\%$. Find the bulk modulus of the rubber ball.
Take the density of water $\rho =1000{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$.

1. $2.66\times {10}^9{\text{N/m}}^2$
2. $3.3\times {10}^9{\text{N/m}}^2$
3. $6.6\times {10}^9{\text{N/m}}^2$
4. $1.33\times {10}^9{\text{N/m}}^2$

Q.

A space of elastic material is taken to bottom of sea (1 km deep). If radius changes by 0.02%, then the bulk modulus of elasticity of material is (Excess pressure = $\rho$gh)

1. $2.4\times {10}^{10}$
2. $3.1\times {10}^{10}$
3. $6\times {10}^{10}$
4. $1.7\times {10}^{10}$

Q.

The ratio of the adiabatic to isothermal elasticities of a triatomic gas is

1. 1

2. 3/4

3. 4/3

4. 5/3

Q.

A solid sphere of radius 20 cm is subjected to a uniform pressure of ${10}^{6}N{m}^{-2}$. If the bulk modulus of the solid is $1.7\times {10}^{11}N{m}^{-2}$, the decrease in the volume of the solid is approximately equal to

1. $0.5c{m}^3$

2. $0.2c{m}^3$

3. $0.4c{m}^3$

4. $0.3c{m}^3$

Q. The bulk modulus of a sphere is ${}^{\prime }{K}^{\prime }$. If it is subjected to uniform pressure ${}^{\prime }{p}^{\prime }$ then fractional decrease in its radius is

1. $\frac{K}{3p}$
2. $\frac{3p}{K}$
3. $\frac{p}{K}$
4. $\frac{p}{3K}$

Q. What is Young's modulus of a material ?

Q.

In isothermal expansion, the pressure is determined by

1. Temperature only

2. Compressibility only

3. Both temperature and compressibility

4. None of these

Q.

What is the purpose of Eigen function?

Q. When pressure of a gas (at ${20}^{\circ }\text{C}$ temperature) is changed from $P_1=1.01\times {10}^5\text{Pa}$ to $P_2=1.165\times {10}^5\text{Pa}$, the volume changes by $10$%. Then the bulk modulus of the gas is

1. $1.55\times {10}^5\text{Pa}$
2. $0.155\times {10}^5\text{Pa}$
3. $1.4\times {10}^5\text{Pa}$
4. $1.01\times {10}^5\text{Pa}$