Chapter 7

Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area \(\mathrm{A}\) and wire 2 has cross-sectional Area \(3 \mathrm{~A}\). If the length of wire 1 increases by on applying force \(\mathrm{F}\). How much force is needed to stretch wire 2 by same amount. (A) \(\mathrm{F}\) (B) \(4 \mathrm{~F}\) (C) \(6 \mathrm{~F}\) (D) \(9 \mathrm{~F}\)

The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied. (A) Length \(100 \mathrm{~cm}\), Diameter \(1 \mathrm{~mm}\) (B) Length \(200 \mathrm{~cm}\), Diameter \(2 \mathrm{~mm}\) (C) Length \(300 \mathrm{~cm}\), Diameter \(3 \mathrm{~mm}\) (D) Length \(50 \mathrm{~cm}\), Diameter \(0.5 \mathrm{~mm}\)

The young's modulus of a wire of length \(\mathrm{L}\) and radius \(\mathrm{r}\) is \(\mathrm{Y}\left(\mathrm{N} / \mathrm{m}^{2}\right)\). If the length and radius are reduced to \(\mathrm{L} / 2\) and \(\mathrm{r} / 2\). Then what will be its young's modulus? (A) \(\mathrm{Y} / 2\) (B) \(\mathrm{Y}\) (C) \(2 \mathrm{Y}\) (D) \(4 \mathrm{Y}\)

On increasing the length by \(0.5 \mathrm{~mm}\) in a steel wire of length \(2 \mathrm{~m}\) and area of cross-section \(2 \mathrm{~mm}^{2}\) the force required is..... \(\left[\mathrm{Y}\right.\) for steel \(\left.=2.2 \times 10^{11} \mathrm{~N} / \mathrm{m}\right]\) (A) \(1.1 \times 10^{5} \mathrm{~N}\) (B) \(1.1 \times 10^{4} \mathrm{~N}\) (C) \(1.1 \times 10^{3} \mathrm{~N}\) (D) \(1.1 \times 10^{2} \mathrm{~N}\)

A stress of \(3.18 \times 10^{8} \mathrm{Nm}^{2}\) is applied to steel rod of length \(1 \mathrm{~m}\) along its length. Its young's modulus is \(2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) Then what is the elongation produced in the rod in \(\mathrm{mm}\) ? (A) \(3.18\) (B) \(6.36\) (C) \(5.18\) (D) \(1.59\)

Two springs \(\mathrm{P} \& \mathrm{Q}\) of force constant \(\mathrm{k}_{\mathrm{P}} \& \mathrm{k}_{\mathrm{Q}}\left(\mathrm{k}_{\mathrm{Q}}=[\mathrm{kp} / 2]\right)\) are stretched by applying force equal magnitude. If the energy stored in \(\mathrm{Q}\) is \(\mathrm{E}\). Then what is the energy stored in \(\mathrm{P} ?\) (A) \(E\) (B) \(2 \mathrm{E}\) (C) \(\mathrm{E} / 2\) (D) \(\mathrm{E} / 4\)

A rubber cord \(10 \mathrm{~m}\) long is suspended vertically. How much does it stretch under its own weight. [Density of rubber is \(1500\left(\mathrm{~kg} / \mathrm{m}^{3}\right), \mathrm{Y}=5 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\), \(\left.\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]\) (A) \(15 \times 10^{-4} \mathrm{~m}\) (B) \(7.5 \times 10^{-4} \mathrm{~m}\) (C) \(12 \times 10^{-4} \mathrm{~m}\) (D) \(25 \times 10^{-4} \mathrm{~m}\)

If \(\mathrm{x}\), longitudinal strain is produced in a wire of young's modulus \(\mathrm{y}\) then energy stored in the material of the wire per unit volume is...... (A) \(\mathrm{yx}^{2}\) (B) \(2 \mathrm{yx}^{2}\) (C) \((1 / 2) \mathrm{y}^{2} \mathrm{x}\) (D) \((1 / 2) \mathrm{yx}^{2}\)

A steel wire of cross-sectional area \(3 \times 10^{-6} \mathrm{~m}^{2}\) can with stand a maximum strain of \(10^{-3}\) Young's modulus of steel is \(2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\). The maximum mass the wire can hold is..... \(\left[\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]\) (A) \(40 \mathrm{~kg}\) (B) \(60 \mathrm{~kg}\) (C) \(80 \mathrm{~kg}\) (D) \(100 \mathrm{~kg}\)

\(\mathrm{A}\) and \(\mathrm{B}\) are two wires. The radius of \(\mathrm{A}\) is twice that of \(\mathrm{B}\). They are stretched by the same load. Then what is the stress on \(\mathrm{B}\) ? (A) Equal to that on \(\mathrm{A}\) (B) Four times that on \(\mathrm{A}\) (C) Two times that on \(\mathrm{A}\) (D) Half that on \(\mathrm{A}\)

When the length of a wire having cross section area \(10^{-6} \mathrm{~m}^{2}\) is streatched by \(0.1 \%\) then tension in it is \(100 \mathrm{~N}\). Young's modulus of material wire is \(\ldots \ldots \ldots\) (A) \(10^{12}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(10^{2}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

Two wires of equal lengths are made of the same material wire A has a diameter that is twice as that of wire \(B\). If identical weights are suspended from the ends of these wires the increase in length is......... (A) Four times for wire \(\mathrm{A}\) as for wire \(\mathrm{B}\). (B) Twice for wire \(\mathrm{A}\) as for wire \(\mathrm{B}\). (C) Half for wire \(\mathrm{A}\) as for wire \(\mathrm{B}\). (D) One-fourth for wire \(\mathrm{A}\) as for wire \(\mathrm{B}\).

An area of a cross-section of rubber string is \(2 \mathrm{~cm}^{3}\). Its length is doubled when stretched with a linear force of \(2 \times 10^{5}\) dynes. What will be young's modulus of the rubber in dynes? (A) \(4 \times 10^{5}\) (B) \(1 \times 10^{5}\) (C) \(2 \times 10^{5}\) (D) \(1 \times 10^{4}\)

A substance breaks down by a stress of \(106 \mathrm{~N} / \mathrm{m}^{2}\). If the density of the material of the wire is \(3 \times 10^{3}\left(\mathrm{~kg} / \mathrm{m}^{3}\right)\) then the length of wire of the substance which will break under its own weight when suspended vertically is......... (A) \(66.6 \mathrm{~m}\) (B) \(60.0 \mathrm{~m}\) (C) \(33.3 \mathrm{~m}\) (D) \(30.0 \mathrm{~m}\)

The temperature of a wire of length 1 meter and area of cross-sectional section \(1 \mathrm{~cm}^{2}\) is increased from \(0^{\circ}\) to \(100^{\circ} \mathrm{C}\). If the rod is not allowed to increase in length. What will be the force required ? \(\left[\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, \mathrm{Y}=10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\right]\) (A) \(10^{3} \mathrm{~N}\) (B) \(10^{4} \mathrm{~N}\) (C) \(10^{5} \mathrm{~N}\) (D) \(10^{9} \mathrm{~N}\)

If longitudinal strain for a wire is \(0.03\) and its poisson's ratio is \(0.5\), then what is its lateral strain ? (A) \(0.003\) (B) \(0.0075\) (C) \(0.015\) (D) \(0.4\)

An aluminum rod [Young's modulus \(=7 \times 10^{9}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) has a breaking strain of \(0.2 \%\) what is the minimum cross-sectional area of the rod in order to support a load of \(10^{4}\) Newtons? (A) \(1 \times 10^{-2} \mathrm{~m}^{2}\) (B) \(1.4 \times 10^{-3} \mathrm{~m}^{2}\) (C) \(3.5 \times 10^{-3} \mathrm{~m}^{2}\) (D) \(7.1 \times 10^{-4} \mathrm{~m}^{2}\)

Two wires of copper having the length in the ratio \(4: 1\) and their radii are as \(1: 4\) are stretched by the same force. What will be the ratio of longitudinal strain in the two wires? (A) \(1: 16\) (B) \(16: 1\) (C) 1:64 (D) \(64: 1\)

A wire elongates by \(1 \mathrm{~mm}\) when a load \(\mathrm{W}\) is hanged from it. If the wire goes ever a pulley and two weight \(\mathrm{W}\) each are hang at the two ends. What will be the elongation of the wire? (in \(\mathrm{mm}\) ) (A) \(2 \ell\) (B) zero (C) \(C / 2\) (D) \(\ell\)

A steel wire is stretched with a definite load. If the young's modulus of the wire is \(\mathrm{Y}\). For decreasing the value of \(\mathrm{Y}\). (A) Radius is to be decreased (B) Radius is to be increased (C) Length is to be increased (D) None of the above

3: A force of \(200 \mathrm{~N}\) is applied at one end of a wire of length \(2 \mathrm{~m}\) and having area of cross-section \(10^{-2} \mathrm{~cm}^{2}\), the other end of the wire is rigidly fixed. If of linear expansion of the wire \(\alpha=8 \times 10^{-6} /{ }^{\circ} \mathrm{C}\) and young's modulus \(\mathrm{Y}=2.2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) and its temperature is increased by \(5^{\circ} \mathrm{C}\) then the increase in the tension of the wire will be.......... (A) \(4.2 \mathrm{~N}\) (B) \(4.4 \mathrm{~N}\) (C) \(2.4 \mathrm{~N}\) (D) \(8.8 \mathrm{~N}\)

A uniform plank of young's modulus \(\mathrm{Y}\) is moved over a smooth horizontal surface by a constant horizontal force \(\mathrm{F}\), The area of cross-section of the plank is \(\mathrm{A}\). What is the compressive strain on its plank in the direction by the force ? (A) (F / AY) (B) \((2 \mathrm{~F} / \mathrm{AY})\) (C) \((1 / 2)(\mathrm{F} / \mathrm{AY})\) (D) (3F / AY)

The length of a wire is \(1.0 \mathrm{~m}\) and the area of cross-section is \(1.0 \times 10^{-2} \mathrm{~cm}^{2}\). If the work done for increase in length by \(0.2 \mathrm{~cm}\) is \(0.4\) joule. Then what is the young's modulus? Of material of the wire ? (A) \(2.0 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(4.0 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(2.0 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(4.0 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

A rubber cord catapult has cross-sectional area \(25 \mathrm{~mm}^{2}\) and initial length of cord is \(10 \mathrm{~cm} .\) It is stretched to \(5 \mathrm{~cm}\) and then released to project a missile of mass \(5 \mathrm{gm}\). Taking \(\mathrm{Y}_{\text {rubber }}=5 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) velocity of projected missile is \(\ldots \ldots .\) (A) \(20(\mathrm{~m} / \mathrm{s})\) (B) \(100(\mathrm{~m} / \mathrm{s})\) (C) \(250(\mathrm{~m} / \mathrm{s})\) (D) \(200(\mathrm{~m} / \mathrm{s})\)

A wire of cross-section \(4 \mathrm{~mm}^{2}\) is stretched by \(0.1 \mathrm{~mm}\) by a certain weight. How far (length) will be wire of same material and length but of area \(8 \mathrm{~mm}^{2}\) stretched under the action of same force. (A) \(0.05 \mathrm{~mm}\) (B) \(0.10 \mathrm{~mm}\) (C) \(0.15 \mathrm{~mm}\) (D) \(0.20 \mathrm{~mm}\)

A copper wire of length \(4 \mathrm{~m}\) and area of cross-section \(1.2 \mathrm{~cm}^{2}\) is stretched with a force of \(4.8 \times 10^{3} \mathrm{~N}\). If young's modulus for copper is \(1.2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\). What will be the length increase of the wire? (A) \(1.33 \mathrm{~mm}\) (B) \(1.33 \mathrm{~cm}\) (C) \(2.66 \mathrm{~mm}\) (D) \(2.66 \mathrm{~cm}\)

If the interatomic spacing in a steel wire is \(3 \AA \&\) \(\mathrm{Y}_{\text {Steel }}=20 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right) .\) The force constant \(=\ldots \ldots \ldots .\) (A) \(6 \times 10^{-2}(\mathrm{~N} / \AA)\) (B) \(6 \times 10^{-9}(\mathrm{~N} / \AA)\) (C) \(6 \times 10^{-5}(\mathrm{~N} / \AA)\) (D) \(6 \times 10^{-5}(\mathrm{~N} / \AA)\)

A wire of length \(2 \mathrm{~m}\) is made from \(10 \mathrm{~cm}^{3}\) of copper. A force \(\mathrm{F}\) is applied so that its length increases by \(2 \mathrm{~mm}\). Another wire of length \(8 \mathrm{~m}\) is made from the same volume of copper. If the force \(\mathrm{F}\) is applied to it, its length will increase by......... (A) \(0.8 \mathrm{~cm}\) (B) \(1.6 \mathrm{~cm}\) (C) \(2.4 \mathrm{~cm}\) (D) \(3.2 \mathrm{~cm}\)

A wire of length \(L\) and radius \(\mathrm{r}\) is rigidly fixed at one end on stretching the other end of the wire a force \(\mathrm{F}\) the increase in its lengths is \(\ell\). If another wire of same material but of length \(2 \mathrm{~L}\) and radius \(2 \mathrm{r}\) is stretched with a force of \(2 \mathrm{~F}\), the increase in its length will be........... (A) \(\varepsilon\) (B) \(2 \ell\) (C) \(\mathrm{C} / 2\) (D) 4

In steel the young's modulus and the strain at the breaking point are \(2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) and \(0.15\) respectively the stress at the breaking point for steel is therefore........... (A) \(1.33 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(1.33 \times 10^{12}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(7.5 \times 10^{-13}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(3 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

Which of the following statement is correct (A) Hooke's law is applicable only within elastic limit. (B) The adiabatic and isothermal elastic constants of a gas area equal. (C) Young's modulus is dimensionless. (D) Stress multiplied by strain is equal to stored energy.

A copper wire and a steel wire of same diameter and length are connected end to end a force is applied, which stretches their combined length by \(1 \mathrm{~cm}\), the two wires will have......... (A) different stresses and strains (B) the same stress and strain (C) the same strain but different stresses (D) the same stress but different strains

A steel ring of radius \(\mathrm{r}\) and cross-section area ' \(\mathrm{A}^{\prime}\) is fitted on to a wooden disc of radius \(\mathrm{R}(\mathrm{R}>\mathrm{r})\) If young's modulus be \(\mathrm{E}\) then what is force with which the steel ring is expanded? (A) \(\mathrm{AE}(\mathrm{R} / \mathrm{r})\) (B) \(\mathrm{AE}[(\mathrm{R}-\mathrm{r}) / \mathrm{r}]\) (C) \((\mathrm{E} / \mathrm{A})[(\mathrm{R}-\mathrm{r}) / \mathrm{R}]\) (D) \([\mathrm{Er} / \mathrm{AR}]\)

A wire of diameter \(1 \mathrm{~mm}\) breaks under a tension of \(100 \mathrm{~N}\). Another wire of same material as that of the first one, but of diameter \(2 \mathrm{~mm}\) breaks under a tension of \(\ldots \ldots \ldots\) (A) \(500 \mathrm{~N}\) (B) \(1000 \mathrm{~N}\) (C) \(10,000 \mathrm{~N}\) (D) \(4000 \mathrm{~N}\)

On applying a stress of \(20 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) the length of a perfect elastic wire is doubled. What will be its Young's modulus ? (A) \(40 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(20 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(10 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(5 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

To keep constant time, watches are fitted with balance wheel made of \(\ldots \ldots \ldots\) (A) invar (B) stainless steel (C) Tungsten (D) platinum

A wire is stretched by \(0.01 \mathrm{~m}\) by a certain force \(\mathrm{F}\). Another wire of same material whose diameter and length are double to the original wire is stretched by the same force? Then what will be its elongation? (A) \(0.005 \mathrm{~m}\) (B) \(0.01 \mathrm{~m}\) (C) \(0.02 \mathrm{~m}\) (D) \(0.002 \mathrm{~m}\)

The Coefficient of linear expansion of brass \& steel are \(\alpha_{1} \&\) \(\alpha_{2}\) If we take a brass rod of length \(\ell_{1} \&\) steel rod of length \(\ell_{2}\) at \(0^{\circ} \mathrm{C}\), their difference in length \(\left(\ell_{2}-\ell_{1}\right)\) will remain the same at a temperature if \(\ldots \ldots \ldots \ldots\) (A) \(\alpha_{1} \ell_{2}=\alpha_{2} \ell_{1}\) (B) \(\ell_{2} \alpha_{1}=\alpha_{2} \ell_{1}\) (C) \(a_{2}^{2} \ell_{1}=a_{2}^{2} \varepsilon_{2}\) (D) \(\alpha_{1} \ell_{1}=\alpha_{2} \mathcal{C}_{2}\)

A rod is fixed between two points at \(20^{\circ} \mathrm{C}\). The Coefficient of linear expansion of material of rad is \(1.1 \times 10^{-5} /{ }^{\circ} \mathrm{C}\) and Young's modulus is \(1.2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\). Find the stress developed in the rod if temperature of rod becomes \(10^{\circ} \mathrm{C}\). (A) \(1.32 \times 10^{7}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(1.10 \times 10^{15}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(1.32 \times 10^{8}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(1.10 \times 10^{6}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

How much force is required to produce an increase of \(0.2 \%\) in the length of a broses wire of diameter \(0.6 \mathrm{~mm}\) (Young's modulus for brass \(=0.9 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (A) Nearly \(17 \mathrm{~N}\) (B) Nearly \(34 \mathrm{~N}\) (C) Nearly \(51 \mathrm{~N}\) (D) Nearly \(68 \mathrm{~N}\)

A \(5 \mathrm{~m}\) long aluminum wire \(\left[\mathrm{Y}=7 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\right]\) of diameter \(3 \mathrm{~mm}\) supports a \(40 \mathrm{~kg}\) mass. In order to have the same elongation in a copper wire \(\mathrm{Y}=12 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) of the same length under the same weight, the diameter should now be in \(m m \ldots \ldots \ldots \ldots\) (A) \(1.75\) (B) \(1.5\) (C) \(2.5\) (D) \(5.0\)

Two similar wires under the same load yield elongation of \(0.1 \mathrm{~mm}\) and \(0.05 \mathrm{~mm}\) respectively. If the area of Cross-section of the first wire is \(4 \mathrm{~mm}^{2}\). Then what is the area of cross - section of the second wire? (A) \(6 \mathrm{~mm}^{2}\) (B) \(8 \mathrm{~mm}^{2}\) (C) \(10 \mathrm{~mm}^{2}\) (D) \(12 \mathrm{~mm}^{2}\)

An iron rod of length \(2 \mathrm{~m}\) and cross-section area of \(50 \mathrm{~mm}^{2}\) stretched by \(0.5 \mathrm{~mm}\), when a mass of \(250 \mathrm{~kg}\) is hung from its lower end. What is young's modulus of the iron rod? (A) \(19.6 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (B) \(19.6 \times 10^{15}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (C) \(19.6 \times 10^{18}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(19.6 \times 10^{20}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

A load \(W\) produces an extension of \(1 \mathrm{~mm}\) in a thread of radius \(r\). Now if the load is made \(4 \mathrm{~W}\) and radius is made \(2 \mathrm{r}\) all other things remaining same the extension will becomes.......... (A) \(4 \mathrm{~mm}\) (B) \(16 \mathrm{~mm}\) (C) \(1 \mathrm{~mm}\) (D) \(0.25 \mathrm{~mm}\)

A steel wire of \(1 \mathrm{~m}\) long and \(1 \mathrm{~mm}^{2}\) cross sectional area \(1 \mathrm{~s}\) hung from rigid end when weight of \(1 \mathrm{~kg}\) is hung from it then change in length will be........... [ \(\left.\mathrm{Y}=2 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\right]\) (A) \(0.5 \mathrm{~mm}\) (B) \(0.25 \mathrm{~mm}\) (C) \(0.05 \mathrm{~mm}\) (D) \(5 \mathrm{~mm}\)

Two wires of same diameter of the same material having the length \(\ell\) and \(2 \ell\). If the force \(\mathrm{F}\) is applied on each, what will be the ratio of the work done in the two wires? (A) \(1: 2\) (B) \(1: 4\) (C) 2: 1 (D) \(1: 1\)

A 5 meter long wire is fixed to the ceiling. A weight of \(10 \mathrm{~kg}\) is hung at the lower end and is 1 meter above the four. The wire was elongated by \(1 \mathrm{~mm}\). What is the stored in the wire due to stretching ? (A) Zero (B) \(0.05\) Joule (C) 100 Joule (D) 500 Joule

If the force constant of a wire is \(\mathrm{k}\). What is the work done in increasing the length of the wire by \(\ell\) ? (A) \([\mathrm{k} \ell / 2]\) (B) \(\mathrm{k} \ell\) (C) \(\left[\mathrm{k} \ell^{2} / 2\right]\) (D) \(\mathrm{k} \ell^{2}\)

Wire \(\mathrm{A}\) and \(\mathrm{B}\) are made from the same material. \(\mathrm{A}\) has twice the diameter and three times the length of \(\mathrm{B}\). If the elastic limits are not reached when each is stretched by the same tension, what is the ratio of energy stored in \(\mathrm{A}\) to that in \(\mathrm{B}\) ? (A) \(2: 3\) (B) \(3: 4\) (C) \(3: 2\) (D) \(6: 1\)

A brass rod of cross sectional area \(1 \mathrm{~cm}^{2}\) and length \(0.2 \mathrm{~m}\) is compressed length wise by a weight of \(5 \mathrm{~kg}\). If young's modulus of elasticity of brass is \(1 \times 10^{11}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) and \(\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\) Then what will be increase in the energy of rod ? (A) \(10^{-5} \mathrm{~J}\) (B) \(2.5 \times 10^{-5} \mathrm{~J}\) (C) \(5 \times 10^{-5} \mathrm{~J}\) (D) \(2.5 \times 10^{-4} \mathrm{~J}\)