Question 1 :
Which property of an object cannot be changed by applying forces?
Question 3 :
Assertion: Strain is a unitless quantity.
Reason: Strain is equivalent to force
Question 4 :
The property of metals which allows them to be drawn into wires is known as :<br/>
Question 5 :
The Young's modulus of a wire of length $L$ and radius $r$ is $Y$. If the length is reduced to $\cfrac{L}{2}$ and radius is $\cfrac{r}{2}$, then the Young's modulus will be
Question 7 :
The property to restore the natural shape or to oppose the deformation is called :
Question 8 :
Assertion: Stress is the internal force per unit area of a body.
Reason: Rubber is more elastic than steel.
Question 12 :
The property of a material due to which shape is changed permanently is known as:<br/>
Question 13 :
According to Hooke's law of elasticity, if stress is increased, then the ratio of stress to strain :
Question 14 :
A wire of length $L$ and area of cross-section $A$, is stretched by a load. The elongation produced in the wire is $l$. If $Y$ is the Young's modulus of the material of the wire, then the force constant of the wire is :
Question 15 :
Fill in the blank.<br/>In a technical sense a substance with a ________ elasticity is one that requires a ______ force to produce a distortion-for example, a steel sphere. <br/><br/>
Question 16 :
If the velocity (V), acceleration (A), and force (F) are taken as fundamental quantities instead of mass (M), length (L) and time (T), the dimensions of Young's modulus (Y) would be
Question 18 :
A toy car travels in a horizontal circle of radius 2a, kept on the track by a radial elastic string of unstretched length a. The period of rotation is T. Now the car is speeded up until it is moving in a circle of radius 3a. Assuming that the string obeys Hooke's law then the new period will be
Question 19 :
A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:
Question 21 :
If two rodes $A$ and $B$ of the same material and length having radii ${r}_{1}$ and ${r}_{2}$ respectively are rigidly fixed at one end are twisted by the same couple applied at the other end, then the ratio of<br>$\left( \cfrac { angle\quad of\quad twist\quad at\quad the\quad end\quad of\quad A }{ angle\quad of\quad twist\quad at\quad the\quad end\quad of\quad B } \right) $ will be
Question 23 : Assertion (A): Steel is more elastic than rubber.<br/>Reason (R) : Under a given deforming force, steel is deformed less than rubber.<div><br/>A) Both Assertion and Reason are true and the reason is correct explanation of the assertion<br/>B)Both Assertion and Reason are true, but reason is not correct explanation of the assertion<br/>C) Assertion is true, but the reason is false<br/>D) Assertion is false, but the reason is true</div>
Question 29 :
The temperature of a wire is doubled. The Young's modulus of elasticity will ?
Question 30 :
For most materials, the Young's modulus is $n$ times the modulus of rigidity, where $n$ is
Question 31 :
Consider the following two statements A and B and identify the correct answer.<br>A) When the length of a wire is doubled, the Young's modulus of the wire is also doubled<br>B) For elastic bodies Poisson's ratio is + Ve and for inelastic bodies Poissons ratio is -Ve
Question 32 :
A copper wire is having length $2m$ and area of cross -section $2mm^2$. Then amount of work done (in joule ) in increasing its length by $0.1mm$ will be (Young's modulus o elasticity for copper $Y=1.2\times 10^{11}Nm^{-2}$
Question 33 :
The stress-strain curve shows a straight line along the third quadrant. What does it depict
Question 34 :
Assertion: The linear portion of the stress-strain curve is the elastic region and the slope is the modulus of elasticity or Young's Modulus.
Reason: Young's Modulus is the ratio of the compressive stress to the longitudinal strain.
Question 35 :
Young's modulis of brass and steel are $10 \times 10^{10}\ N/m$ and $2\times 10^{11}\ N/m^2$, respectively. A brass wire and a steel wire of the same length are extended by $1mm$ under the same force. The radii of brass and steel wires are $R_B$ and $R_S$ respectively. Then<br>
Question 36 :
An iron bar of length $L$, cross-section $A$ and Young's modulus $Y$ is pulled by a force $F$ from ends so as to produce an elongation $l$. Which of the following statements is correct ?
Question 37 :
A river $10\ m$ deep is flowing at $5\ m/s$. The shearing stress between horizontal layers of the river is $(\eta = 10^{-3} SI\ units)$.
Question 38 :
A $15kg$ mass fastened to the end of a steel wire of unstretched length $1.0m$ is whirled in a vertical circle with an angular velocity of $2rev$ ${s}^{-1}$ at the bottom of the circle. The cross-section of the wire is $0.05{cm}^{2}$. The elongation of the wire when the mass is at the lowest point of its path is<br>(Take $g=10m{ s }^{ -2 },{ Y }_{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 }\quad $)
Question 39 :
Assertion: The linear portion of the stress-strain curve is the elastic region and the slope is the modulus of elasticity or Young's Modulus.
Reason: Young's Modulus is the ratio of the compressive stress to the longitudinal strain.
Question 40 :
Two wires of the same material and length are stretched by the same force. Their masses are in the ratio $3 : 2$. Their elongations are in the ratio<br>
Question 41 : A vertical steel post of diameter $25 cm$ and length $2.5 m$ supports a weight of $8000 kg$. Find the change in length produced.<div>(Given $Y=2\times 10^{11}Pa$)<br/></div>
Question 42 :
The compressibility of water is $6\times { 10 }^{ -10 }{ N }^{ -1 }{ m }^{ 2 }$. If one litre is subjected to a pressure of $4\times { 10 }^{ 7 }N{ m }^{ -2 }$, the decrease in its volume is then<br/>
Question 43 :
Bulk Modulus, Pressure, Force, Stress, which one of these wont have the same unit as the others?
Question 44 :
A long spring is stretched by $2 cm$ and its potential energy is $U$. If the spring is stretched by $10 cm$; its potential energy will be (in terms of $U$)
Question 45 :
The length of two wires are in the ratio $3 : 4$.Ratio of the diameters is $1:2$; young's modulus of the wires are in the ratio $3:2$; If they are subjected to same tensile force, the ratio of the elongation produced is
Question 46 :
For a given material, the Young's modulus is $2.4$ times that of the modulus of rigidity. Its Poisson's ratio is
Question 47 :
A volume of $10^{-3}m^{3}$ is subjected to a pressure of 10 atmospheres. The change in volume is $10^{-6}m^{3}$. Bulk modulus of water is (Atmosphere pressure = 1x10$^{5} N / m^{2}$ ) :
Question 49 :
If a rubber ball is taken at the depth of 200 m in a pool its volume decreases by 0.1% If the density of the water is $\displaystyle 1\times 10^{3}kg/m^{3}\: $and$\: g=10m/s^{2}$ then the volume elasticity in $\displaystyle N/m^{2}$ will be
Question 50 :
The value of shear stress which is induced in the shaft due to applied couple varies
Question 51 :
A rubber rope of length $8\ m$ is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young's modulus of elasticity of rubber $= 5\times 106\ N/m$ and density of rubber $= 1.5\times 10^{3} kg/ m^{3}$. Take $g = 10\ m/s^{2})$.
Question 52 :
If the temperature of a wire of length $2m$ and area of cross section $1cm^2$ is increased from $0^0C$ to $80^0C$ and is not allowed to increase in length, then required for it is $Y = {10^{10}}\,N/{m^2}$
Question 53 :
A solid sphere of radius $R$ made of material of bulk modulus $K$, is surrounded by a liquid in a cylindrical container. A massless piston of area $A$ floats on the surface of liquid. When a mass $m$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere $\delta R/R$ is :
Question 54 :
The extension of a wire by the application of a load is $0.3 cm$. The extension in the wire of the same material but of double the length and half the radius of cross section in cm is
Question 55 :
In $CGS$ system, the Young's modulus of a steel wire is $2 \times 10^{12}$. To double the length of a wire of unit cross section area, the force required is <br><br>
Question 56 :
A steel wire of length $4m$ is stretched by a force of $100N$. The work done to increase the length of the wire by $2mm$ is
Question 57 :
When temperature of a gas is $20^{\circ}C$ and pressure is changed from $p_{1} = 1.01\times 10^{5} Pa$ to $p_{2} = 1.165\times 10^{5} Pa$, the volume changes by $10\%$. The bulk modulus is
Question 58 :
The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept inside the container is $1:4$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all the temperature?
Question 59 :
Assertion (A) : Bulk modulus of elasticity (K) represents incompressibility of the material.<br/>Reason (R) : $K= -\frac{\Delta P}{\Delta V/V}$, where symbols have their standard meaning.
Question 60 :
The Bulk moduli of Ethanol, Mercury and water are given as $0.9, 25$ and $2.2$ respectively in units of $10^9/ Nm^{-2}$. For a given value of pressure, the fractional compression in volume is $\displaystyle \frac{\Delta V}{V}$. Which of the following statements about $\displaystyle \frac{\Delta V}{V}$ for these three liquids is correct?<br>
Question 61 :
Two wires of the same material (young's modules 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 in equilibrium is <br>
Question 62 :
A rubber ball is brought into 200 m deep water, its volume is decreased by 0.1% then volume elasticity coefficient of the material of ball will be:<br/>$(Given\ \rho = 10^3 kg/m^3$ and $ g = 9.8 ms^{-2})$
Question 64 :
The length of a metal wire is $l_1$ when the tension in it is $T_1$ and is $I_2$ when the tension is $T_2$. The natural length of the wire is?
Question 65 :
In Searle's experiment to find Young's modulus the diameter of wire is measured as $d=0.05cm$, length of wire is $l=125cm$ and when a weight,$m=20.0kg$ is put, extension in wire was found to be $0.100cm$. Find the maximum permissible error in Young's modulus $(Y)$. Use:$Y=\displaystyle\frac{mgl}{(\pi/4)d^2x}$.
Question 66 :
A uniform pressure p is exerted on all sides of a solid cube at temperature ${t^0}C$. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube y and the bulk modulus is B.
Question 67 :
There are two wires of the same material. There radii and lengths are both in the ratio $1:2$. If the extensions produce dare equal, what is the ratio of the loads?
Question 68 : <p>A steel rope has length $L$, area of cross-section $A$, Young's modulus $Y$ and density as $ d$. It is pulled on a horizontal frictionless floor with a constant horizontal force $F=\dfrac{dALg}{2}$ applied at one end. Find the strain at the midpoint.</p>
Question 69 :
A mass m is hanging from a wire of cross sectional are A and length L. Y is young's modulus of wire. An external force F is applied on he wire which is then slowly further pulled down by $\triangle x$ from its equilibrium position. Find the work done by the force F that the wire exerts on the mass:
Question 70 :
A metal wire of length $1\ m$ and cross-section area $2\ mm^{2}$ and Young's modulus of elasticity $Y=4\times 10^{11}\ N/m^{2}$ is stretched by $2\ mm$. Then
Question 71 :
The length of a metal wire is $l_1$ when the tension in it is $F_1$ and $l_2$ when the tension is $F_2$. Then original length of the wire is:
Question 72 :
A steel rope has length $L$, area of cross-section $A$, Young's modulus $Y$. [$Density = d$]. If the steel rope is vertical and moving with the force acting vertically up at the upper end, find the strain at a point $\displaystyle \frac{L}{3}$ from lower end.
Question 73 :
The length of a uniform metal wire is observed to be $l_1$ and $l_2$ under the stretching forces $F_1$ and $F_2$. The natural length of the wire is
Question 74 :
A tension of $20\ N$ is applied to a copper wire of cross sectional area $0.01 cm^2$, Young's Modulus of copper is $1.1\times 10^{11} N/m^2$ and Poisson's ratio is 0.32. The decrease in cross sectional area of the wire is:
Question 75 :
The length of a metal wire is $l_{1}$ when the tension in it is $T_{1}$ and is $l_{2}$ when the tension is $T_{2}$. The natural length of wire is
Question 76 :
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $\left(\displaystyle\frac{dr}{r}\right)$, is?
Question 77 :
In a Young's double slit experiment with sodium light, slits are 0.589 m apart. The angular separation of the maximum from the central maximum will be (given $\lambda =589$nm,):
Question 78 :
When an elastic material with Young's modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is
Question 79 :
A solid sphere of radius 20cm is subjected to a uniform pressure of $ 10^{6}$ $N m^{-2}$. If the bulk modulus is $1.7 \times 10^{11}$ $N m^{-2}$, the decrease in the volume of the solid is approximately equal to:
Question 80 :
A uniform cylindrical wire is subjected to a longitudinal tensile stress of $5\times 10^{7} N/m^{2}$. Young's modulus of the material of the wire is $2\times 10^{11} N/m^{2}$. The volume change in the wire is $0.02\%$. The fractional change in the radius is
Question 81 :
A thick uniform rubber rope of density $1.5\ g\ cm^{-3}$ and Young's modulus $5 \times 10^{6}$ $N m^{-2}$ has a length of $8 m$. When hung from the ceiling of a room, the increase in length of the rope due to its own weight will be
Question 82 :
Two wires of different material and radius have their length in ratio of $1:2.$ if these were stretched by the same force$,$ the strain produced will be in the ratio$.$
Question 83 :
$32 g$ of $O_{2}$ is contained in a cubical container of side $1 m$ and maintained at a temperature of $127 ^{0} C$. The isothermal bulk modulus of elasticity of the gas in terms of universal gas constant $R$ is
Question 84 :
<span class="wysiwyg-font-size-small">A wire that obeys Hooke's law is of length $l_1$ when it is in equilibrium under a tension $F_1$. Its length becomes $l_2$ when the tension is increased of $F_2$. The energy stored in the wire during this process is</span><br>
Question 85 :
A brass rod of length $1 \ m$ is fixed to a vertical wall at one end, with the other end keeping free to expand. When the temperature of the rod is increased by $120^{\circ}C$ , the length increases by $3 \ cm$. What is the strain?
Question 86 : An increase in pressure required to decreases the $200$ litres volume of a liquid by $0.004\%$ in the container is<div>(Bulk modulus of the liquid $=2100$ MPa).</div>
Question 87 :
A wire elongates by $1 mm$ when a load W is hanged from it. lf the wire goes over a pulley and two weights $\mathrm{W}$ each are hung at the two ends, the elongation of the wire will be (in mm):<br/>
Question 88 :
A pendulum of a uniform wire of cross-sectional area $A$ has time period $T.$ When an additional mass $M$ is added to its bob, the time period changes to $T_M$ . If the Young's modulus of the material of the wire is $Y$ then $\displaystyle \frac {1} {Y} $ is equal to :<br>($g$ = gravitational acceleration)
Question 89 :
In performing an experiment to determine the Young's modulus Y of steel, a student can record the following values:<br>length of wire l$=(\ell_{0}\pm\Delta$l$){m}$<br>diameter of wire ${d}=({d}_{0}\pm\Delta {d})$ mm<br>force applied to wire ${F}$=$({F}_{0}\pm\Delta {F}){N}$<br>extension of wire ${e}=({e}_{0}\neq\Delta {e})$ mm<br>In order to obtain more reliable value for Y, the followlng three techniques are suggested. <br>Technique (i) A shorter wire ls to be used.<br>Technique (ii) The diameter shall be measured at several places with a micrometer screw gauge.<br>Technique (iii) Two wires are made irom the same ntaterial and of same length. One is loaded at a fixed weight and acts as a reference for the extension of the other which is load- tested<br>Which of the above techniques is/are useful?<br>
Question 90 :
A cube of sponge rubber with edge length 5 cm has a force of 2 N applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of 1 mm, find the shear modulus for the sponge rubber.
