CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 13 - MCQExams.com

In solids, inter-atomic forces are
  • Totally repulsive
  • Totally attractive
  • Combination of (a) and (b)
  • None of these
Two wires of the same material have lengths in the ratio $$1:2$$ and their radii are in the ratio $$1:\sqrt{2}$$. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio
  • $$2:\sqrt{2}$$
  • $$\sqrt{2}:2$$
  • $$1:1$$
  • $$1:2$$
An area of cross-section of rubber string is $$2cm^2$$. Its length is doubled when stretched with a linear force of $$2 \times 10^5 dynes$$. The Young's modulus of the rubber in $$dyne/cm^{2}$$ will be
  • $$4 \times 10^{5}$$
  • $$1 \times 10^{5}$$
  • $$2 \times 10^{5}$$
  • $$1 \times 10^{4}$$
If a spring is extended to length $$l$$ then according to Hook's law
  • $$F=kl$$
  • $$F=\dfrac{k}{l}$$
  • $$F=k^2l$$
  • $$F=\dfrac{k^2}{l}$$
Two wires $$A$$ and $$B$$ have equal lengths and are made of the same material, but the diameter of wire $$A$$ is twice that of wire $$B$$. Then, for a given load:
  • the extension of $$B$$ will be four times that of $$A$$
  • the extensions of $$A$$ and $$B$$ will be equal
  • the strain in $$B$$ is four times that in $$A$$
  • the strains in $$A$$ and $$B$$ will be equal
A uniform rod of mass m, length L , area of cross-section A and is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity $$\omega $$ in a horizontal plane. If Y the Youngs modulus of the material of rod, the increase in its length due torotation of rod is :
  • $$\frac{m\omega ^{2}L^{2}}{AY}$$
  • $$\frac{m\omega ^{2}L^{2}}{2AY}$$
  • $$\frac{m\omega ^{2}L^{2}}{3AY}$$
  • $$\frac{2m\omega ^{2}L^{2}}{AY}$$

The equation of a stationary wave in a metal rod is given by $$y=0.002\displaystyle \sin\frac{\pi x}{3}\sin 1000t$$, where $$\mathrm{x}$$ is in cm and $$\mathrm{t}$$ is in second. The maximum tensile stress at a point $$\mathrm{x}=2\mathrm{c}\mathrm{m}$$ (Young's modulus $$\mathrm{Y}$$ of material of rod $$=8\times 10^{11}dyne/cm^{2})$$ will be
  • $$\displaystyle \frac{\pi}{3}\times 10^{8}dyne/cm^{2}$$
  • $$\displaystyle \frac{4\pi}{3}\times 10^{8}dyne/cm^{2}$$
  • $$\displaystyle \frac{8\pi}{3}\times 10^{8}dyne/cm^{2}$$
  • $$\displaystyle \frac{2\pi}{3}\times 10^{8}dyne/cm^{2}$$
A copper wire is held at the two ends between two rigid supports. At $$30^{\mathrm{o}}\mathrm{C}$$, the wire is just taut,with negligible tension. If $$Y=13\times 10^{11}Nm^{-2}, \alpha =1.7\times 10^{-5}(^{\circ}C)^{-1}$$ and density $$ \rho=9\times 10^{3}kgm^{-3}$$, then the speed of transverse wave in this wire at $$10^{o}$$C is:
  • $$ 90 ms^{-1} $$
  • $$70 ms^{-1}$$
  • $$60 ms^{-1}$$
  • $$100 ms^{-1}$$
 In performing an experiment to determine the Young's modulus Y of steel, a  student can record the following values:
length of wire l$$=(\ell_{0}\pm\Delta$$l$$){m}$$
diameter of wire $${d}=({d}_{0}\pm\Delta {d})$$ mm
force applied to wire $${F}$$=$$({F}_{0}\pm\Delta {F}){N}$$
extension of wire $${e}=({e}_{0}\neq\Delta {e})$$ mm
In order to obtain more reliable value for Y, the followlng three techniques are suggested.
Technique (i) A shorter wire ls to be used.
Technique (ii) The diameter shall be measured at several places with a micrometer screw gauge.
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
Which of the above techniques is/are useful?
  • i and ii only
  • ii and iii only
  • i only
  • iii only
One end of a horizontal thick copper wire of length $$2L$$ and radius $$2R$$ is welded to an end of another horizontal thin copper wire of length $$L$$ and radius $$R$$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is:
  • $$0.25$$
  • $$0.50$$
  • $$2.00$$
  • $$4.00$$
$$32 g$$ 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
  • $$127 R$$
  • $$400 R$$
  • $$200 R$$
  • $$560 R$$
A uniform rod of mass m, length L, area of cross-section A and Youngs modulus Y hangs from a rigid support. Its elongation under its own weight will be:
  • zero
  • mgL/2YA
  • mgL/YA
  • 2mgL/YA.
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):
  • $$1/2$$
  • $$1 $$
  • $$2 $$
  • zero
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.
  • $$(dgL)/2Y$$
  • $$(dgL)/4Y$$
  • $$(dgL)/6Y$$
  • $$(dgL)/8Y$$
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
  • $$0.25\times 10^{-4}$$
  • $$0.5\times 10^{-4}$$
  • $$0.1\times 10^{-4}$$
  • $$1.5\times 10^{-4}$$
A slightly conical wire of length L and end radii $$r_1$$ and $$r_2$$ is stretched by two forces F and F applied parallel to the length in opposite directions and normal to the end faces. If Y denotes Young's modulus, then the extension produced is:
  • $$\displaystyle \frac{FL}{\pi r_1 r_2Y}$$
  • $$\displaystyle \frac{FLY}{\pi r_1 r_2}$$
  • $$\displaystyle \frac{FL}{\pi r_1 Y}$$
  • $$\displaystyle \frac{FL}{\pi r_1^{2}Y}$$
The speed of a traverse wave travelling on a wire having a length $$50\space cm$$ and mass $$50\space g$$ is $$80\space ms^{-1}$$. The area of cross-section of the wire is $$1\space mm^2$$ and its Young's modulus is $$16\times10^{11}\space Nm^{-2}$$. Find the extension of the wire over natural length.
  • $$2\space cm$$
  • $$2\space mm$$
  • $$0.2\space mm$$
  • $$0.02\space mm$$
A copper rod of length $$l$$ is suspended from the ceiling by one of its ends. Find the elongation $$\Delta l$$ of the rod due to its own weight.
  • $$\displaystyle\Delta l=\frac{1}{2}\frac{\rho gl^2}{E}$$
  • $$\displaystyle\Delta l=\frac{1}{3}\frac{\rho gl^2}{E}$$
  • $$\displaystyle\Delta l=\frac{1}{4}\frac{\rho gl^2}{E}$$
  • $$\displaystyle\Delta l=\frac{1}{5}\frac{\rho gl^2}{E}$$
Six identical uniform rods $$PQ, QR, RS, ST, TU$$ and $$UP$$ each weighing W are freely joined at their ends to form a hexagon. The rod $$PQ$$ is fixed in a horizontal position and middle points of $$PQ$$ and $$ST$$ are connected by a vertical string. The tension in string is
138063_499051a63fca4d559bf30b8427c7b4af.png
  • $$W$$
  • $$3W$$
  • $$2W$$
  • $$4W$$
Two opposite forces $$F_1 = 120N \:and \:F_2 = 80N$$ act on an heavy elastic plank of modulus of elasticity $$y=2\times 10^{11}N/m^2$$ and length $$L = 1m$$ placed over a smooth horizontal surface. The cross-sectional area of plank is $$A = 0.5m^2$$. If the change in the length of plank is (in nm )

78559.jpg
  • 1
  • 0.5
  • 5
  • 2
A metal wire of length L, area of cross section A and Young's modulus Y is stretched by a variable force F such that F is always slightly greater than the elastic forces of resistance in the wire. Then the elongation of the wire is $$l$$.
  • The work done by F is $$\displaystyle \frac{YAl^2}{2L}$$
  • The work done by F is $$\displaystyle \frac{YAl^2}{L}$$
  • The elastic potential energy stored in the wire is $$\displaystyle \frac{YAl^2}{2L}$$
  • No heat is produced during the elongation
The length of a metal is $$l_1$$ when the tension in it is $$T_1$$ and is $$l_2$$ when the tension is $$T_2$$. The original length of the wire is  :
  • $$\displaystyle\frac{l_1+l_2}{2}$$
  • $$\displaystyle\frac{l_1T_2+l_2T_1}{T_1+T_2}$$
  • $$\displaystyle\frac{l_1T_2-l_2T_1}{T_2-T_1}$$
  • $$\displaystyle \sqrt{T_1T_2l_1l_2}$$
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:$$Y=\displaystyle\frac{mgl}{(\pi/4)d^2x}$$.
  • $$6.3\%$$
  • $$5.3\%$$
  • $$2.3\%$$
  • $$1\%$$
 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
  • $$R_S=\sqrt 2R_B$$
  • $$R_S=\dfrac{R_B}{\sqrt 2}$$
  • $$R_S=4R_B$$
  • $$R_S=\dfrac{R_B}{4}$$
Two wire 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 given load
  • The extension of B will be four times that of A
  • the extension of A and B will be equal
  • the strain in B is four times that in A
  • the strains in A and B will be equal
If the ratio of lengths, radii and Young's modulus of steel and brass wires shown in the figure are a, b and c respectively, the ratio between the increase in lengths of brass and steel wires would be :

467585.png
  • $$\dfrac{{ b }^{ 2 }}{2c}$$
  • $$\dfrac{bc}{{ 2a }^{ 2 }}$$
  • $$\dfrac{{ ba }^{ 2 }}{2c}$$
  • $$\dfrac{{ 2b }^{ 2 }c}{a}$$
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:
  • $$\dfrac{l_1F_1+l_2F_2}{F_1+F_2}$$
  • $$\dfrac{l_2-l_1}{F_2-F_1}$$
  • $$\dfrac{l_1F_2-l_2F_1}{F_2-F_1}$$
  • $$\dfrac{l_1F_1-l_2F_2}{F_2-F_1}$$
A copper wire and a steel wire of the same length and same cross section are joined end to end to form a composite wire. The composite wire is hung from a rigid support and a load is suspended from the other end. If the increase in length of the composite wire is $$2.4\ mm$$, then the increase in lengths of steel and copper wires are:
$$(Y_{cu} = \, 10 \times \, 10^{10} \, N/m^2, \, Y_{steel} = \, 2 \times \, 10^{11} \, N /m^2)$$  
  • $$1.2\ mm$$, $$1.2\ mm$$
  • $$0.6\ mm$$, $$1.8\ mm$$
  • $$0.8\ mm$$, $$1.6\ mm$$
  • $$0.4\ mm$$, $$2.0\ mm$$
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.The decrease in cross sectional area of the wire is:
  • $$1.16\times 10^{-6}cm^2$$
  • $$1.16\times 10^{-5}m^2$$
  • $$1.16\times 10^{-4}m^2$$
  • $$1.16\times 10^{-3}cm^2$$
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
  • $$\dfrac {l_{1} + l_{2}}{2}$$
  • $$\sqrt {l_{1}l_{2}}$$
  • $$\dfrac {l_{1}T_{2} - l_{2}T_{1}}{T_{2} - T_{1}}$$
  • $$\dfrac {l_{1}T_{2} + l_{2}T_{1}}{T_{2} + T_{1}}$$
An Aluminium and Copper wire of same cross sectional area but having lengths in the ratio $$2 : 3$$ are joined end to end. This composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in length of the composite wire is $$2.1 \ mm$$, the increase in lengths of Aluminium and Copper wires are : [$$\displaystyle { Y }_{ Al }=20\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } }$$ and $$\displaystyle { Y }_{ Cu }=12\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } }$$]
  • $$0.7 \ mm; 1.4\  mm$$
  • $$0.9\  mm; 1.2\  mm$$
  • $$1.0\  mm; 1.1\  mm$$
  • $$0.6 \ mm; 1.5\  mm$$
The load versus elongation graph of four wires of same length and of the same material is shown in figure. The thinnest wire is represented by the line :
643524_7f6bd6d53af149fc81e45102fc202a53.jpg
  • $$OA$$
  • $$OB$$
  • $$OC$$
  • $$OD$$
The Young's modulus of a material is $$2\times { 10 }^{ 11 }N/{ m }^{ 2 }$$ and its elastic limit is $$1.8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$. For a wire of $$1m$$ length of this material, the maximum elongation achievable is
  • $$0.2mm$$
  • $$0.3mm$$
  • $$0.4mm$$
  • $$0.5mm$$
A rigid bar of mass $$15 kg$$ is supported symmetrically by three wires each $$2 m$$ long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension? (Given E for copper = $$110\times 10^{9} N/m^{2}$$ and E for iron = $$190\times 10^{9} N/m^{2}$$).
  • $$12.6 : 2$$
  • $$1.31 : 1$$
  • $$4.65 : 3$$
  • $$2.69 : 4$$
Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1 :The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is
  • 3 : 1
  • 9 : 1
  • 27 : 1
  • 81 : 1
When a metallic wire is stretched with a tension $$\displaystyle { T }_{ 1 }$$ its length is $$\displaystyle { l }_{ 1 }$$ and with a tension $$\displaystyle { T }_{ 2 }$$ its length is $$\displaystyle { l }_{ 2 }$$. The original length of the wire is:
  • $$\displaystyle \frac { { l }_{ 1 }{ T }_{ 2 }-{ l }_{ 2 }{ T }_{ 1 } }{ { T }_{ 2 }-{ T }_{ 1 } } $$
  • $$\displaystyle \frac { { l }_{ 1 }{ T }_{ 2 }+{ l }_{ 2 }{ T }_{ 1 } }{ { T }_{ 2 }+{ T }_{ 1 } } $$
  • $$\displaystyle \sqrt { { l }_{ 1 }{ l }_{ 2 } } $$
  • $$\displaystyle \frac { { l }_{ 1 }{ l }_{ 2 } }{ 2 } $$
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
  • $$9.6 \times 10^{-2}$$
  • $$19.2 \times 10^{-2}$$
  • $$9.6 \times 10^{-3}$$
  • $$9.6 $$
A steel wire of length $$4.5m$$ and cross-sectional area $$3\times { 10 }^{ -5 }{ m }^{ 2 }$$ stretches by the same amount as a copper wire of length $$3.5m$$ and cross-sectional area of $$4\times { 10 }^{ -5 }{ m }^{ 2 }$$ under a given load. The ratio of the Young's modulus of steel to that of copper is:
  • $$1.3$$
  • $$1.5$$
  • $$1.7$$
  • $$1.9$$
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?
  • $$\displaystyle\frac{mg}{3 Ka}$$
  • $$\displaystyle\frac{mg}{Ka}$$
  • $$\displaystyle\frac{Ka}{mg}$$
  • $$\displaystyle\frac{Ka}{3 mg}$$
Two metal wire 'P' and 'Q' of same length and material are stretched by same load. Their masses are in the ratio $$m_1 : m_2$$. The ratio of elongations of wire 'P' to that of 'Q' is
  • $$m_{1}^{2} : m_{2}^{2}$$
  • $$m_{2}^{2} : m_{2}^{1}$$
  • $$m_2 : m_1$$
  • $$m_1 : m_2$$
An amusement park ride consists of airplane shaped cars attached to steel rods. Each rod has a length of 20.0 m and a cross-sectional area of 8.00 $$cm^2$$. Young's modulus for steel is $$2 \, \times \, 10^{11} \, N/m^2.$$
b. When operating, the ride has a maximum angular speed of $$\sqrt{1}$$9/5 rad/s. How much is the rod stretched (in mm) then? 

984372_ea3e2e965d304ae482e8795b729b2b61.png
  • 0.38 mm
  • 0.55 mm
  • 0.45 mm
  • 0.34 mm
The rubber cord of a catapult has cross-section area $$2m{m}^{2}$$ and a total unstretched length $$15cm$$. It is stretched to $$18cm$$ and then released to project a particle of mass $$3g$$. Calculate the velocity of projection if $$Y$$ for rubber is $$8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$.
  • $$56.5{ms}^{-1}$$
  • $$10{ms}^{-1}$$
  • $$20{ms}^{-1}$$
  • $$40{ms}^{-1}$$
A student did an experiment to determine the Youngs modulus $$(Y)$$ of a nylon thread, $$2.00\ m$$ in length, using Searles method. A Vernier callipers having a least count of $$0.01\ mm$$ was used to measure the diameter of the thread. The length and extensions were measured by using a scale with a least count of $$1\ mm$$. The data obtained by the student are shown in the table below. Assume the uncertainty in force to be $$0.01\ N$$.
Length of the thread$$1994\ mm$$
Force$$0.32\ N$$
Extension of the thread$$95\ mm$$
Diameter of the thread$$0.04\ mm$$
Choose the correct alternative(s).
  • The student reports $$Y$$ to be about $$5GPa$$
  • The reported uncertainty in $$Y$$ is $$54$$%
  • Measuring the extension using a travelling microscope with a least count of $$0,1\ mm$$ would improve the accuracy of the result by at most $$1$$%
  • The stress is $$1.8\ GPa$$
The density of water at the surface of the ocean is $$\rho$$ and atmospheric pressure is $${P}_{0}$$. If the bulk modulus of water is $$K$$, what is the density of ocean water at a depth where the pressure is then$$n{P}_{0}$$?
  • $$\cfrac { \rho K }{ K-n{ P }_{ 0 } } \quad $$
  • $$ \cfrac { \rho K }{ K+n{ P }_{ 0 } } $$
  • $$\cfrac { \rho K }{ K-(n-1){ P }_{ 0 } } $$
  • $$\cfrac { \rho K }{ K+(n-1){ P }_{ 0 } } $$.
A solid sphere of radius $$R$$, made up of a 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. When a mass $$M$$ is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is
  • $$\dfrac {Mg}{2AK}$$
  • $$\dfrac {Mg}{3AK}$$
  • $$\dfrac {Mg}{AK}$$
  • $$\dfrac {2Mg}{3AK}$$
If the ratio of diameters, lengths and Young's moduli of steel and brass wires shown in the figure are $$p,q$$ and $$r$$ respectively. Then the corresponding ratio of increase in their lengths would be:
936991_7c95ffc772014bbba808dadbdabda759.png
  • $$\cfrac { 3q }{ 5{ p }^{ 2 }r } $$
  • $$\cfrac { 5q }{ 3{ p }^{ 2 }r } $$
  • $$\cfrac { 3q }{ 5{ p }^{ }r } $$
  • $$\cfrac { 5q }{ { p }^{ }r } $$
A uniform pressure P is exerted on all sides of a solid cube at temperature t $$^oC$$. 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 cube is $$\alpha$$ and the bulk modulus is K.
  • $$\dfrac{P}{\alpha K}$$
  • $$\dfrac{P\alpha}{K}$$
  • $$\dfrac{PK}{\alpha}$$
  • $$\dfrac{2K}{P}$$
A given quantity of an ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of the gas is?
  • $$\dfrac{2}{3}P$$
  • P
  • $$\dfrac{3}{2}P$$
  • $$2P$$
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? 
  • $$0$$
  • $$10$$
  • $$20$$
  • $$30$$
Two wires are made of the same material and have the same volume. However $$wire\ 1$$ has cross-sectional area $$A$$ and $$wire\ 2$$ has cross-sectional area $$3A.$$ If the length of $$wire\ 1$$ is increases by $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch $$wire\ 2$$ by the same amount?
  • $$6F$$
  • $$9F$$
  • $$F$$
  • $$4F$$
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