Young's Modulus of Elasticity

Q. The Young’s modulus of a wire of length L and radius r is $\frac{YN}{m^2}$. If the length and radius are reduced to $\frac{L}{2}$ and $\frac{r}{2}$, then its Young's modulus will be

1. 
2. 
3. 
4. 

Q.

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1:4$, the ratio of their diameters is:

1. $\sqrt{2}:1$

2. $1:\sqrt{2}$

3. $1:2$

4. $2:1$

Q. One end of a long metallic wire of length L, area of cross-section A and Young’s modulus Y is tied to the ceiling. The other end is tied to a massless spring of force constant k. A mass m hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by

1. 
2. 
3. 
4. 

Q.

Two wires of the same material and same length but diameters in the ratio $1:2$ are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio:

Q.

A wire fixed at the upper end stretches by length $\mathrm{l}$ by applying a force $\mathrm{F}$. The work done in stretching is:

1. $\frac{\mathrm{F}}{2\mathrm{l}}$

2. $\mathrm{Fl}$

3. $\frac{2\mathrm{F}}{\mathrm{l}}$

4. $\frac{\mathrm{Fl}}{2}$

Q.

The diameter of a brass rod is $4mm$ and Youngs modulus of brass is $9\times {10}^{10}\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$m^2$}\right.$. The force required to stretch it by $0.1\%$ of its length is

1. $360\mathrm{\pi N}$

2. $36N$

3. $144\times {10}^{3}N$

4. $36\mathrm{\pi }\times {10}^5\mathrm{N}$

Q.

A wire of area of cross section 3.0 $m{m}^2$and natural length 50 cm is fixed at one end and a mass of 2.1 kg is hung from the other end. Find the elastic potential energy stored in the wire in steady state. Young's modulus of the material of the wire = $1.9\times {10}^{11}N{m}^{-2}.Takeg=10m{s}^{-2}$

1. 10^-4 J

2. 2 x 10^-4 J

3. 3 x 10^-4 J

4. 0.5 x 10^-4 J

Q. When a rod is heated but prevented from expanding, the stress developed is independent of

1. length of rod
2. material of the rod
3. rise in temperature
4. none of these

Q. Two wires of the same material (Young’s modulus Y) and same length L but radii R and 2R respectively are joined end to end and a weight w is suspended from the combination as shown in the figure. The elastic potential energy in the system is

1. 
2. 
3. 
4. 

Q. The Young’s modulus of three materials are in the ratio 2:2:1. Three wires made of these materials have their cross-sectional areas in the ratio 1:2:3. For a given stretching force the elongation's in the three wires are in the ratio

1. 1:2:3
2. 3:2:1
3. 5:4:3
4. 6:3:4

Q.

Two separate wires A and B are stretched by $2mm$ and $4mm$ respectively, when they are subjected to a force of $2N$. Assume that both the wires are made up of the same material and the radius of wire B is $4$ times that of the radius of wire A. The length of the wires A and B are in the ratio of $a:b$, Then $\frac{a}{b}$ can be expressed as $\frac{1}{x}$. What is the value of where $x$?

Q.

A force F doubles the length of wire of cross-section ‘$a$’. What is the Young modulus of wire ?

Q. If work done by the system is 300J when 100cal heat is supplied to it. Find the change in d internal energy during the process.

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.

If the force constant of a wire is $k$, the work done in increasing the length $L$ of the wire by $l$ is

1. 3Kl

2. 2Kl

3. 

4. 

Q.

Two aluminium wires have lengths 1 m and 2 m and their diameters are d and d if they are stretched by applying equal forces the ratio of increase in their lengths will be

Q.

Two rods of different materials, having coefficients of linear expansion ${\alpha }_1$ and ${\alpha }_2$ and Young's moduli $Y_1$ and $Y_2$ respectively, are fixed between two rigid walls. The rods are heated to the same temperature. There is no bending of the rods. If ${\alpha }_1:{\alpha }_2=2:3$, the thermal stress developed in the two rods will be equal provided $Y_1:Y_2$ is equal to

1. 2:3

2. 3:2

3. 4:9

4. 1:1

Q. One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire in attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Find the longitudinal strain in both the wires. Area of cross section of each wire is $0.005c{m}^2$ and Young modulus of the metal is $2.0\times {10}^{11}N{m}^{-2}.$ Take $g=10m{s}^{-2}.$

1. ${10}^{-5},5\times {10}^{-5}$
2. ${10}^{-4},3\times {10}^{-4}$
3. ${10}^{-3},2\times {10}^{-3}$
4. None of the above

Q. A wire is stretched under a force. If the wire suddenly snaps, the temperature of the wire

1. decreases
2. remains the same
3. increases
4. first decreases then increases

Q. The Young's modulus of a wire of length L and radius r is Y N/m. If the length and radius are reduced to $\frac{L}{2}$ and $\frac{r}{2}$, then its Young's modulus will be

1. Y/2
2. Y
3. 2Y
4. 4Y

Q.

When shearing force is applied on a body, then the elastic potential energy is stored in it. On removing the force, this energy is most likely to get converted into

1. heat energy

2. Remains as potential energy

3. Can not Say

4. kinetic energy

Q. Why do telephone wires sag during summer?

Q.

Three blocks, each of same mass m, are connected with wires $w_1$and $w_2$ of same cross-sectional area a Youngs modulus Y. Neglecting friction the strain developed in wire $w_2$ is

1. 

2. 

3. 

4. 

Q. If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

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

Q.

A steel wire of length 4.7m and cross section area $3\times {10}^{-6}{m}^2$ stretches by the same amount as a copper wire of length 3.5 m and cross-section area $4\times {10}^{-6}{m}^2$ under a given load. The ratio of Young's modulus of steel to that of copper is

1. 1.8

2. 3.6

3. 0.6

4. 8.7

Q. If the density of the material increases, the value of Young's modulus

1. Increases
2. Decreases
3. First increases then decreases
4. First decreases then increases

Q. The work done in stretching an elastic wire per unit volume is or strain energy in a stretched string is

1. Stress X Strain
2. 2 X strain X stress
3. Stress/Strain
4. 

Q. The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

1. 
2. 
3. 
4. 

Q.

Two wires A and B are of the same material. Their lengths are in the ratio 1:2 and diameters are in ratio 2:1. When stretched by force F^A and F^B respectively, they get an equal increase in lengths. Find the ratio of F^A / F^B.

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