Volume Strain

Q.

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is</br>

1. 0.01

2. 0.06

3. 0.02

4. 0.03

Q. What is the bulk modulus for a perfect rigid body?

Q. Find the volumetric strain of the spherical ball of radius $10\text{cm}$ whose volume changes by $4.18\times {10}^{-6}{\text{m}}^3$ under the application of bulk stresses.

1. $1.0$
2. $0.1$
3. $0.01$
4. $0.001$

Q. When a force is applied at one end of an elastic wire, it produces a strain E in the wire. If Y is the Young's modulus of the material of the wire, the amount of energy stored per unit volume of the wire is given by

1. $Y\times E$
2. $\frac{1}{2}(Y\times E)$
3. $Y\times E^2$
4. $\frac{1}{2}(Y\times E^2)$

Q.

Which of the following forces is non conservative one?

1. $3\hat{i}+4\hat{j}$

2. $4x\hat{i}+3y\hat{j}$

3. $y^2\hat{i}+x^2\hat{j}$

4. $3x^2\hat{i}+4y^2\hat{j}$

Q. Find the volumetric strain of the spherical ball of radius $10\text{cm}$ whose volume changes by $4.18\times {10}^{-6}{\text{m}}^3$ under the application of bulk stresses.

1. $1.0$
2. $0.1$
3. $0.01$
4. $0.001$

Q. A body submerged in water experiences which of the following types of strain?

1. Longitudinal strain
2. Shear strain
3. None of these
4. Volumetric strain

Q. A material has Poisson's ratio $0.5$. If a uniform rod made of the material suffers a longitudinal strain of $2\times {10}^{-3}$, what is the percentage increase in volume?

1. $2\%$
2. $5\%$
3. $0\%$
4. $4\%$

Q. A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

1. $0.01$
2. $0.06$
3. $0.02$
4. $0.03$

Q. A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain developed is

1. 0.01
2. 0.06
3. 0.02
4. 0.03

Q. A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain developed is

1. 0.02
2. 0.06
3. 0.03
4. 0.01

Q.

The combustion chamber of a bike has an area of cross-section $16{\text{cm}}^2$. A pressure of $400\text{Pa}$ acts on it. Find the force exerted on the bike.

Q. A uniform bar of length of ${}^{\prime }{L}^{\prime }$ and cross sectional area of 'A' is subjected to a tensile load of ${}^{\prime }{F}^{\prime }{.}^{\prime }{Y}^{\prime }$ be the Young Modulus and ${}^{\prime }{\sigma }^{\prime }$ be the Poisson's ratio. Then volumetric strain is:

1. $\frac{F}{AY}\sigma$
2. $\frac{F}{AY}(1-2\sigma )$
3. $\frac{F}{AY}(2-\sigma )$
4. $\frac{F}{AY}(1-\sigma )$

Q. A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

1. $0.01$
2. $0.06$
3. $0.02$
4. $0.03$

Q. If B is the bulk modulus of a metal and a pressure p is applied uniformly on all sides of the metal, with density D, then the fractional increases in density is given by

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

Q. When a body is wholly or partly immersed in a liquid it experiences.

1. An up-thrust or down-thrust depending on the density of the liquid
2. An up-thrust
3. A down-thrust
4. None of the above

Q. A uniform cube is subjected to volume compression. Each side gets decreased by 1%, then the bulk strain is

1. $0.01$
2. $0.03$
3. $0.06$
4. $0.09$

Q.

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is</br>

1. 0.01

2. 0.06

3. 0.02

4. 0.03

Q. Find the volumetric strain of the spherical ball of radius $10\text{cm}$ whose volume changes by $4.18\times {10}^{-6}{\text{m}}^3$ under the application of bulk stresses.

1. $1.0$
2. $0.1$
3. $0.01$
4. $0.001$

Q. Assertion :The maximum stress value below which the strain is fully recoverable is called the elastic limit. Reason: All materials are elastic to some extent but the degree varies.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A spherical ball of radius $r$ and relative density $0.5$ is floating in equilibrium in water with half of its immersed in water. The work done in pushing the ball down so that whole of it is just immersed in water is $1\rho$ is the density of water-

1. $0.25\rho rg$
2. $0.5\rho rg$
3. $\frac{4}{3}\pi r^3\rho g$
4. $\frac{5}{12}\pi r^4\rho g$

Q. Young's modulus of material of wire is '$Y$' and strain energy per unit volume is '$E$', then the strain is

1. $\sqrt{\frac{Y}{2E}}$
2. $\sqrt{2EY}$
3. $\sqrt{\frac{2E}{Y}}$
4. $\sqrt{\frac{E}{Y}}$

Q. A brass sphere weighs $100gm.wt$ in air. It is suspended by a thread in a liquid of specific gravity $=0.8$. If the specific gravity of brass is $8$, the tension in the thread in newtons is :

1. $0.0882$
2. $8.82$
3. $0.882$
4. $0.00882$

Q. When the tension in a metal wire is $F_1$ its length is $L_1$ and then the tension in the wire is $F_2$ the length is $L_2$. The natural length of the wire is

1. $L_1{F}_2=L_2{F}_1$
2. $\frac{L_1{F}_2+L_2{F}_1}{F_2+F_1}$
3. $\frac{L_1{F}_2-L_2{F}_1}{F_2+F_1}$
4. $L_1{F}_1+L_2{F}_2$

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. In case of steel wire or a metal wire, the elastic limit is reached when :

1. The load is more than the weight of wire
2. None of the above
3. Elongation is inversely proportional to the tension
4. The wire just break

Q. The coefficient of linear expansion of a crystal in one direction is ${\alpha }_1$ and that in every direction perpendicular to it is ${\alpha }_2$. Then, the coefficient of cubical expansion of the crystal is

1. ${\alpha }_1+{\alpha }_2$
2. $2{\alpha }_1+{\alpha }_2$
3. ${\alpha }_1+2{\alpha }_2$
4. None of these

Q. The line of action of the buoyant force acts through the centroid of :

1. submerged body
2. volume of the floating body
3. volume of the fluid vertically above the body
4. displaced volume of the fluid

Q. A sphere of radius $10cm$ and mass $25kg$ is attached to the lower end of steel wire of length $5m$ and diameter of $4mm$ which is suspended from the ceiling of a room. The point of support is $521cm$ above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest position.

Q. A wire of conical shape of length $L$ and end radii $r_1$, and $r_2$ is stretched by two forces F applied parallel to the length in opposite directions normal to the end faces as shown. If $Y$ denotes the Young's modulus elasticity then extension produced is

1. $\frac{FL}{\pi r_1{r}_{2}Y}$
2. $\frac{FL}{2\pi r_1{r}_{2}Y}$
3. $\frac{FL}{\pi r_1^{2}Y}$
4. $\frac{2FL}{\pi r_1{r}_{2}Y}$