Longitudinal Strain

Q.

State the laws for writing SI units.

Q.

What is the Youngs modulus of copper wire?

Q.

Two wires A and B of the same material have their lengths in the ratio of 1:2 and their diameters in the ratio of 2:1. If they are stretched with the same force, the ratio of the increase in the length of A to that of B will be

1. 1:2

2. 1:4

3. 4:1

4. 1:8

Q. A uniform heavy rod of weight W, cross-sectional area A and length L is hanging from a fixed support. Young modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.

1. 

2. 

3. 

4. 

Q. In an experiment, brass and steel wires of length $1\text{m}$ each with areas of cross-section $1{\text{mm}}^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produce a net elongation of $0.2\text{mm}$ is
[Take Young’s modulus for steel and brass as $120\times {10}^9{\text{N/m}}^2$ and $60\times {10}^9{\text{N/m}}^2$respectively]

1. $1.2\times {10}^6{\text{N/m}}^2$
2. $0.2\times {10}^6{\text{N/m}}^2$
3. $8\times {10}^6{\text{N/m}}^2$
4. $4.0\times {10}^6{\text{N/m}}^2$

Q. If the ratio of lengths, radii and Young's modulus of steel and brass wires in the figure are $a,b$ and $c$ respectively, then the corresponding ratio of increase in their lengths would be

1. $\frac{2a^{2}c}{b}$
2. $\frac{3c}{2a{b}^2}$
3. $\frac{3a}{2b^{2}c}$
4. $\frac{2ac}{b^2}$

Q.

A rod of length $2\text{m}$ rests on smooth horizontal floor. If the rod is heated from $0^{\circ }C$ to ${20}^{\circ }C$. Find the longitudinal strain developed?

1. ${10}^{-3}$
2. $2\times {10}^{-3}$
3. Zero
4. None

Q. A wooden wheel of radius $R$ is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross - sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$ and its Young's modulus is $Y$, the force that one part of the wheel applies on the other part is-

1. $2\pi SY\alpha \Delta T$
2. $SY\alpha \Delta T$
3. $2SY\alpha \Delta T$
4. $\pi SY\alpha \Delta T$

Q.

Which is more elastic glass or steel?

Q. At ${40}^{\circ }\text{C}$, a brass wire of $1\text{mm}$ radius is hung from the ceiling. A small mass, $M$ is hung from the free end of the wire. When the wire is cooled down from ${40}^{\circ }\text{C}\text{to}{20}^{\circ }\text{C}$ it regains its original length of $0.2\text{m}$. The value of $M$ is close to:
(Coefficient of linear expansion and Young's modulus of brass are ${10}^{-5}{/}^{\circ }\text{C}$ and ${10}^{11}{\text{Nm}}^{-2}$ respectively; $g=10{\text{ms}}^{-2})$

1. $0.5\text{kg}$
2. $6.3\text{kg}$
3. $9\text{kg}$
4. $1.5\text{kg}$

Q. A toy cart is tied to the end of an unstretched string of length $‘l^{\prime }$, when revolved, the toy cart moves in horizontal circle with radius $‘2l^{\prime }$ and time period $T_1$. If it is speeded until it moves in horizontal circle of radius $‘3l^{\prime }$ with period $T_2$, relation between $T_1$ and $T_2$ is (Hooke’s law is obeyed)

1. $T_2=\frac{2}{\sqrt{3}}{T}_1$
2. $T_2=\sqrt{\frac{3}{2}}{T}_1$
3. $T_2=\sqrt{\frac{2}{3}}{T}_1$
4. $T_2=\frac{\sqrt{3}}{2}{T}_1$

Q. The kinetic energy correction factor for laminar flow in a circular pipe is:

1. 1.23
2. 1.54
3. 2
4. None of these

Q. Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$, the ratio of the lengths of the strings is:–

1. $1:3$
2. $2:1$
3. $3:2$
4. $3:4$

Q. A wire increases by ${10}^{-3}$ times of its length when a stress of $1\times {10}^8{\text{Nm}}^{-2}$ is applied to it in the longitudinal direction. Ratio of longitudinal stress and longitudinal strain in the wire is

1. ${10}^{11}{\text{Nm}}^{-2}$
2. $5.2\times {10}^4{\text{Nm}}^{-2}$
3. $2\times {10}^6{\text{Nm}}^{-2}$
4. ${10}^8{\text{Nm}}^{-2}$

Q. An Indian rubber cord $L\text{m}$ long and area of cross-section $A{\text{m}}^2$ is suspended vertically. Density of rubber is $D{\text{kg/m}}^3$ and Young's modulus of rubber is $E{\text{N/m}}^3.$ If the wire extends by $l\text{m}$ under its own weight, then extension $l$ is

1. $L$
2. $L^{2}Dg/2E$
3. $L^{2}Dg/E$
4. $L^{2}Dg/4E$

Q. Two wires of length $l$, radius $r$ and length $2l$, radius $2r$ respectively having same young's modulus are hung with a weight $mg$ as shown in figure. The net elongation is

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

Q.

How do you know if a spring obeys Hookes Law?

Q. A massless wire $2\text{m}$ in length suspended vertically stretches by $10\text{mm}$ when mass of $10\text{kg}$ is attached to the lower end. The elastic potential energy gained by the wire is (Take $g=10{\text{m/s}}^2$)

1. $0.5\text{J}$
2. $5\text{J}$
3. $50\text{J}$
4. $500\text{J}$

Q.

What Is Meant By Elasticity?

Q.

Name the force acting on a stretched rubber band.

Q. Choose the incorrect option about linear strain

1. Both (a) and (b)
2. None of these
3. It is a ratio of the change in dimension of the body due to the deformation to its original dimension in the direction of the force applied.
4. It is dimensionless quantity.

Q. A rod, of length $L$ at room temperature and uniform area of cross-section $A$, is made of a metal having coefficient of linear expansion $\alpha {}^{\circ }{\text{C}}^{-1}$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta T\text{K}$. Young's modulus, $Y$, for this metal is:

1. $\frac{F}{A\alpha \Delta T}$
2. $\frac{2F}{A\alpha \Delta T}$
3. $\frac{F}{2A\alpha \Delta T}$
4. $\frac{F}{A\alpha (\Delta T-273)}$

Q. Steel wire of length ‘L’ at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is ${10}^{–5}/°C,$ Young’s modulus of steel is ${10}^{11}N/m^2$ and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m; in kg is nearly.

2. 3

Q. Each of the three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm^{2} and Young modulus 2 \times 10^{11} N~m^{2}. Neglect friction. Find the longitudinal strain developed in wire B. Take $g=10m{s}^{-2}.$

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

Q.

The diagram shows a force – extension graph for a rubber band. Consider the following statements

I. Steel has similar force extension curve

II. Rubber does not return to its original length after it is stretched

III. The rubber band will get heated if it is stretched and released

Which of these can be deduced from the graph?

1. I only
2. III only
3. I and III
4. II and III

Q. The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of$5\times {10}^{-4}$is $kJ/m^3$. Assume that material is elastic upto the linear strain of $5\times {10}^{-4}$.

Q. A metal wire is stretched beyond its elastic limit and released, then wire

1. loses its elastic property completely and it will not contract.
2. will contract to its original length.
3. will contract till it achieves its elastic limit.
4. will contract but its final length will be greater than original length.

Q. Two wires $A$ and $B$ have equal lengths and are made of the same material, but the diameter of $A$ is twice that of wire $B$. Then, for a given load,

1. the extension of $B$ will be four times that of $A$.
2. the extension of $A$ and $B$ will be equal.
3. the strain in $B$ is four times that in $A$.
4. the strains in $A$ and $B$ will be equal.

Q. A wire of cross-section area $2{\text{mm}}^2$ is stretched by $0.1\text{mm}$ by a certain force. How far (length) will the wire of same material and length but area $8{\text{mm}}^2$ stretch under the action of same force?

1. $0.25\text{mm}$
2. $0.005\text{mm}$
3. $0.025\text{mm}$
4. $0.05\text{mm}$

Q. A weight Mg is suspended from the middle of a rope whose ends are at the same level. The minimum tension required to completely straighten the rope is