Young's Modulus of Elasticity

Q.

What will happen to the potential energy of the spring when it is compressed or stretched?

Q.

How do you find the Youngs modulus from a load extension graph?

Q. When the tension in a metal wire is $T_1$, its length is $l_1$. When the tension is $T_2$, its length is $l_2$. The natural length of wire is

1. $\frac{T_2}{T_1}(l_2+l_2)$
2. $T_1{l}_1+T_2{l}_2$
3. $\frac{l_1{T}_2-l_2{T}_1}{T_2-T_1}$
4. $\frac{l_1{T}_2+l_2{T}_1}{T_2+T_1}$

Q. The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

1. $Y_B=2Y_A$
2. $Y_A=Y_B$
3. $Y_B=3Y_A$
4. $Y_A=3Y_B$

Q. What is the percentage increase in length of a wire having diameter $1.5\text{mm}$, stretched by a force of $50\text{kg-wt}$?
(Young's modulus of elasticity of wire $\left(Y\right)=15\times {10}^{11}{\text{dyne/cm}}^2\text{and}g=10{\text{m/s}}^2$)

1. $0.19$
2. $0.019$
3. $1.9$
4. $19$

Q.

A spring is compressed. Does the potential energy of the compressed spring increase or decrease?

Q. The proportional limit of steel is $8\times {10}^8{\text{N/m}}^2$ and its young modulus is $2\times {10}^{11}{\text{N/m}}^2.$ The maximum elongation, a one meter long steel wire can be given without exceeding the proportional limit is

1. $2\text{mm}$
2. $4\text{mm}$
3. $1\text{mm}$
4. $8\text{mm}$

Q. A block of mass $3\text{kg}$ produces an extension of $1\text{mm}$ in a wire of length $4\text{m}$ and diameter $4\text{mm}$ when suspended at one end. The Young's modulus of the material of the wire will be (Assume: $g=10{\text{m/s}}^2\text{and}\pi =3$)

1. ${10}^{10}{\text{N/m}}^2$
2. $4\times {10}^{10}{\text{N/m}}^2$
3. $3\times {10}^{10}{\text{N/m}}^2$
4. $5.88\times {10}^{10}{\text{N/m}}^2$

Q.
Calculate the tension:

1. 20/3 N
2. 40/3 N
3. 20 N
4. 80/3 N

Q. The load versus elongation graph of four wires of equal length of the same material is shown in the figure. The line representing the thinnest wire is

1. $A$
2. $B$
3. $C$
4. $D$

Q. Stress developed in the stretched copper wire is $6\times {10}^5{\text{N/m}}^2$. If young's modulus of copper wire is $1.2\times {10}^{11}{\text{N/m}}^2$, find the energy stored per unit volume in the stretched wire.

1. $0.5{\text{J/m}}^3$
2. $1.5{\text{J/m}}^3$
3. $2.5{\text{J/m}}^3$
4. $3{\text{J/m}}^3$

Q. A thin rod of negligible mass, length $0.5\text{m}$ and area of cross-section $4\times {10}^{-6}{\text{m}}^2$, suspended vertically from one end. The rod is cooled down and it can contract by $5\times {10}^{-4}\text{m}$ but prevented from contracting by attaching a mass at the lower end. Choose the correct option(s).
(Given: Take young's modulus of rod $Y={10}^{11}{\text{N/m}}^2,g=10{\text{m/s}}^2)$

1. Value of mass is $80\text{kg}$
2. Value of mass is $40\text{kg}$
3. Energy stored in the rod is $0.1\text{J}$
4. Energy stored in the rod is $0.2\text{J}$

Q.

Which material has the highest Youngs modulus?

Q. The force required to stretch a steel wire of $1c{m}^2$ cross - section to 1.1 times its length would be $(Y=2\times {10}^{11}N{m}^{-2})$

1. $2\times {10}^{6}N$
2. $2\times {10}^{3}N$
3. $2\times {10}^{-6}N$
4. $2\times {10}^{-7}N$

Q. The diameter of a brass wire is 0.6 mm and Y is $9\times {10}^{6}N{m}^{-2}.$The force which will increase its length by 0.2% is about

1. 100 N
2. 51 N
3. 25 N
4. none of these

Q. Two wires, one of copper and the other of steel are of the same length and cross-section. They are welded together to form a long wire. On suspending a weight at its one end, the increment in length is found to be $3\text{cm}$. If Young's modulus of steel is double that of copper, the increment in steel wire will be

1. $1\text{cm}$
2. $2\text{cm}$
3. $2.5\text{cm}$
4. $1.5\text{cm}$

Q. Two wires A and B have the same length and area of cross section. But Young’s modulus of A is two times the Young’s modulus of B. Then the ratio of force constant of A to that of B is

1. 1
2. 2
3. $\frac{1}{2}$
4. $\sqrt{2}$

Q. A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

1. $Y^2$
2. Y
3. $\frac{1}{Y}$
4. $\frac{1}{Y^2}$

Q. A student plots a graph from the readings obtained on performing the experiment for determination of Young's modulus of a metal wire but he forgets to put the labels on the graph. The quantities on $x$ and $y-$ axis (respectively) shown in the graph may be:

1. Weight hung and length increased
2. Stress applied and length increased.
3. Stress applied and strain developed.
4. Length increased and weight hung.

Q.

Two wires of same diameter of the same material having the length l and 2l. If the force F is applied on each, the ratio of the work done in the two wires will be

1. 1 : 2

2. 1 : 4

3. 2 : 1

4. 1 : 1

Q. To break a wire, a force of ${10}^6\frac{N}{m^2}$ is required. If the density of the material is $3\times {10}^{3}kg/m^3,$ then the length of the wire which will break by its own weight will be

1. 34 m
2. 30 m
3. 300 m
4. 3 m

Q. When a block of mass $2\text{kg}$ is suspended by a long wire of length $1\text{m}$, the length of wire becomes $1.02\text{m}$. The elastic potential energy stored in wire is
(Take $g=10m/s^2$)

1. $0.1\text{J}$
2. $0.2\text{J}$
3. $0.4\text{J}$
4. $0.8\text{J}$

Q. Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are $y_1$ and $y_2$ respectively. The equivalent Young’s modulus will be

1. $Y_1+Y_2$
2. $\frac{Y_1+Y_2}{2}$
3. $\frac{Y_1{Y}_2}{Y_1+Y_2}$
4. $\sqrt{Y_1{Y}_2}$

Q. A light rod with uniform cross-section of ${10}^{-4}{m}^2$ is shown in the adjoining figure. The rod consists of three different materials whose lengths are 0.1 m, 0.2 m and 0.15 m respectively and whose Young's modulii are $2.5\times {10}^{10}\frac{N}{m^2},4\times {10}^{10}\frac{N}{m^2}$ and $1\times {10}^{10}\frac{N}{m^2}$ respectively.
The displacement of point B will be

1. $24\times {10}^{-6}m$
2. $9\times {10}^{-6}m$
3. $4\times {10}^{-6}m$
4. $1\times {10}^{-6}m$

Q. The pressure that has to be applied to the ends of a steel wire of length $10\text{cm}$ to keep its length constant when its temperature is raised by ${100}^{\circ }\text{C}$ is:-
Given: $Y=2\times {10}^{11}{\text{N/m}}^2$ and $\alpha =1.1\times {10}^{-5}{/}^{\circ }\text{C}$

1. $2.2\times {10}^9\text{Pa}$
2. $2.2\times {10}^7\text{Pa}$
3. $2.2\times {10}^8\text{Pa}$
4. $2.2\times {10}^6\text{Pa}$

Q. If in case $A$, elongation in wire of length $L$ is $\Delta L$, then for the same wire, elongation in case $B$ will be

1. $4\Delta L$
2. $2\Delta L$
3. $\Delta L$
4. $\frac{\Delta L}{2}$

Q. The Young’s modulus of brass and steel are $10\times {10}^{10}N{m}^{-2}and2\times {10}^{11}N{m}^{-2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_B$ and $R_s$ respectively. Then

1. $R_A=\sqrt{2}{R}_B$
2. $R_S=\frac{R_B}{\sqrt{2}}$
3. $R_S=4R_B$
4. $R_S=\frac{R_B}{4}$

Q. A sphere of radius $1.00\text{cm}$ is placed in the path of a parallel beam of light of large aperture. The intensity of the light is $0.50{\text{W/cm}}^2.$ If the sphere partially absorbs $(\alpha =0.25)$ the radiation falling on it, find the force exerted by the light beam on the sphere.

1. $9.3\times {10}^{-7}\text{N}$
2. $5.2\times {10}^{-7}\text{N}$
3. $8.5\times {10}^{-7}\text{N}$
4. $9.16\times {10}^{-9}\text{N}$

Q. A metal wire having poisson ratio $1/4$ and young's modulus $4\times {10}^{10}{\text{N/m}}^2$ is stretched by a force, which produces a lateral strain of $0.01\%$ in it. The elastic potential energy stored per unit volume in wire is (in ${\text{J/m}}^3$)

1. $2500$
2. $3200$
3. $6400$
4. $1250$

Q. The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

1. $Y_B=2Y_A$
2. $Y_A=Y_B$
3. $Y_B=3Y_A$
4. $Y_A=3Y_B$