CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 14 - MCQExams.com

The ice storm in the state of Jammu strained many wires to the breaking point. In a particular situation, the transmission towers are separated by $$500\ m$$ of wire. The top grounding wire $$15^{o}$$ from horizontal at the towers, and has a diameter of $$1.5cm$$. The steel wire has a density of $$7860\ kg\ m^{-3}$$. When ice (density $$900\ kg\ m^{-3}$$) built upon the wire to a diameter $$10.0\ cm$$, the wire snapped. What was the breaking stress (force/ unit area) in $$N\ m^{-2}$$ in the wire at the breaking point? You may assume the ice has no strength.
  • $$7.4\ \times 10^{7}\ N\ m^{-2}$$
  • $$4.5\ \times 10^{8}\ N\ m^{-2}$$
  • $$2.6\ \times 10^{6}\ N\ m^{-2}$$
  • $$1.15\ \times 10^{7}\ N\ m^{-2}$$
A spherical ball contracts in volume by $$0.01\%$$ when subjected to a normal uniform pressure of $$100$$ atmospheres. The bulk modulus of its material in dynes$$/cm^2$$ is?
  • $$10\times 10^{12}$$
  • $$100\times 10^{12}$$
  • $$1\times 10^{12}$$
  • $$2\times 10$$
The length of a wire increases by $$8mm$$ when a weight of $$5kg$$ is suspended from it. If other things remain the same but the radius of the wire is doubled, what will be the increase in its length?
  • $$5mm$$
  • $$2mm$$
  • $$7mm$$
  • $$9mm$$
A student performs an experiment to determine the Young's modulus of a wire, exactly $$2m$$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $$0.8$$mm with an uncertainty of $$0.05 mm$$ at a load of exactly $$1.0$$kg. The student also measures the diameter of the wire to be $$0.4mm$$ with an uncertainty of $$0.01mm$$. Take $$g = 9.8 m s^{-2}$$ (exact). The Young's modulus obtained from the reading is:
  • $$(2.0 \  \bar+  \ 0.3) \times 10^{11} N m^{-2}$$
  • $$(2.0 \  \bar+ \ 0.2) \times 10^{11} N m^{-2}$$
  • $$(2.0 \  \bar+  \ 0.1) \times 10^{11} N m^{-2}$$
  • $$(2.0 \  \bar+ \ 0.05) \times 10^{11} N m^{-2}$$
When a metal wire is stretched by a load, the fractional change in its volume $$\left(\dfrac{\Delta V}{V}\right)$$ is proportional to.
  • $$\dfrac{\Delta l}{l}$$
  • $$\left(\dfrac{\Delta l}{l}\right)^2$$
  • $$\sqrt{\dfrac{\Delta l}{l}}$$
  • None of these
A load is supported using three wires of same cross section area as shown. Then for :
List - IList - II
pEqual tensile stress in all wires1$$Y_{2}$$ = 2$$Y_{1}$$
qEqual tension in all wires2$$Y_{2}$$ = 4$$Y_{1}$$
rEqual elastic potential energy in all wires
3$$Y_{2}$$ = 8$$Y_{1}$$
sEqual elastic potential energy per unit volume in all wires4$$Y_{2}$$ = 16$$Y_{1}$$


1025666_b24959ad3509460ea714a5b458941b8f.png
  • P- 2, Q- 3, R- 1, S- 4
  • P- 1, Q- 4, R- 2, S- 3
  • P- 3, Q- 2, R- 4, S- 1
  • P- 2, Q- 2, R- 3, S- 4
A uniform wire of length $$L$$ and radius $$r$$ is twisted by an angle $$\alpha$$. If modulus of rigidity of the wire is $$\eta$$, then the elastic potential energy stored in wire, is 
  • $$\dfrac { \pi \eta { r }^{ 4 }\alpha }{ 2{ L }^{ 2 } }$$
  • $$\dfrac { \pi \eta { r }^{ 4 }{ \alpha }^{ 2 } }{ 4{ L } }$$
  • $$\dfrac { \pi \eta { r }^{ 4 }\alpha }{ 4{ L }^{ 2 } }$$
  • $$\dfrac { \pi \eta { r }^{ 4 }{ \alpha }^{ 2 } }{ 2{ L } }$$
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:
  • $$mg\triangle x+\dfrac{YA}{2L}(\triangle x)^2$$
  • $$mg\triangle x+\dfrac{YA(\triangle x)^2}{L}$$
  • $$mg\dfrac{\triangle x }{2}+\dfrac{YA(\triangle x)^2}{L}$$
  • $$mg\dfrac{\Delta x}{2}+\dfrac{YA(\Delta x)^2}{2L}$$
Two wires of the same radius and material and having length in the ratio $$8.9:7.6$$ are stretched by the same force. The strains produced in the two cases will be in the ratio:
  • $$1:1$$
  • $$8.9:1$$
  • $$1:7.6$$
  • $$1:3.2$$
Breaking stress for steel is $$F/A$$, where $$A$$ is the area of cross-section of steel wire. A body of mass $$M$$ is tied at the end of the steel wire of length $$L$$ and whirled in a horizontal circle. The maximum number of revolution it can make per second is:
  • $$\sqrt { \dfrac { FA }{ { 4\pi }^{ 2 }ML } }$$
  • $$\sqrt { \dfrac { F }{ { 4\pi }^{ 2 }MLA } }$$
  • $$\sqrt { \dfrac { F }{ { 4\pi }^{ 2 }ML } }$$
  • $$\sqrt { \dfrac { { 4\pi }^{ 2 } }{ MLA } }$$
 A mild steel wire of length $$2l$$ meter cross-sectional area $$A\,{m^2}$$ is fixed horizontally between two pillars. A small mass $$m \ kg$$ is suspended from the mid point of the wire. If extension in wire are within elastic limit. Then depression at the mid point of wire will be
  • $${\left( {\frac{{Mg}}{{YA}}} \right)^{1/3}}$$
  • $${\left( {\frac{{Mg}}{{IA}}} \right)^{1/3}}$$
  • $${\left( {\frac{{Mg{l^3}}}{{YA}}} \right)^{1/3}}$$
  • $$\frac{{Mg}}{{2YA}}$$
Two wires of equal length and cross-section are suspended as shown in figure. Their young's modulus are $$Y_1$$ and $$Y_2$$ respectively. Their equivalent young's modulus of elasticity is :
1108292_55643b56e1194ffc9f914c6400dc0b5d.PNG
  • $$Y_1+Y_2$$
  • $$\dfrac{Y_1 +Y_2}2$$
  • $$Y_1-Y_2$$
  • $$Y_1Y_2$$
The Young's modulus of brass and steel are respectively $$1.0\times {10}^{10}N/{m}^{2}$$ and $$2\times {10}^{10}N/{m}^{2}$$. A brass wire and a steel wire of the same length are extended by $$1\ mm$$ under the same force, the radii of brass and steel wires are $${R}_{B}$$ and $${R}_{S}$$ respectively. Then 
  • $${R}_{S}=\sqrt{2}{R}_{B}$$
  • $${R}_{S}=\cfrac{{R}_{B}}{\sqrt{2}}$$
  • $${R}_{S}=4{R}_{B}$$
  • $${R}_{S}=\cfrac{{R}_{B}}{4}$$
A solid sphere of radius R made of a material of bulk modulus B surrounded by a liquid in a cylindrical container.A massless  piston of area A floats on the surface of the liquid. Find the fractional decreases in the radius of the sphere $$ \left( \frac { d R }{ R }  \right)  $$ when a mass M is placed on the piston to compress the liquid:
  • $$ \left( \dfrac { 3Mg }{ AB } \right) $$
  • $$ \left( \dfrac {2 Mg }{ AB } \right) $$
  • $$ \left( \dfrac { Mg }{ 3AB } \right) $$
  • $$ \left( \dfrac { Mg }{ 2AB } \right) $$
A uniform rod of length L, has a mass per unit length $$\lambda$$ and area of cross-section A. The elongation in the rod is l due to its own weight, if it is suspended from the ceiling of a room.The Young's modulus of the rod is 
  • $$\dfrac{ \lambda\,g L^2}{ 2 Al}$$
  • $$\dfrac{3 \lambda\,g L^2}{Al}$$
  • $$\dfrac{2 \lambda\,g L}{Al}$$
  • $$\dfrac{ \lambda\,g L^2}{Al}$$
If $$\delta$$ is the depression produced in beam of length $$L$$, breath $$b$$ and thickness $$d$$, when a load is placed at the mid point, then
  • $$\delta \propto L^3$$
  • $$\delta \propto \dfrac{1}{b^3}$$
  • $$\delta \propto \dfrac{1}{d}$$
  • All of these
A metallic ring of radius $$2cm$$ and cross sectional area $$4cm^{2}$$ is fitted into a wooden circular disc of radius $$4cm$$.If the Young's module of the material of the ring is $$2 \times 10^{11}N/m^2$$, the metal ring expand is:
  • $$2 \times 10^7N$$
  • $$8 \times 10^7N$$
  • $$4 \times 10^7N$$
  • $$6 \times 10^7N$$
The normal density of mercury is $$p$$ and its bulk modulus is $$B$$. The increase in density of gold when a pressure $$p$$ is applied uniformly on all sides is:
  • $$\dfrac{p^{P}}{B}$$
  • $$\dfrac{2p^{p}}{B}$$
  • $$\dfrac{p^{B}}{B}$$
  • $$\dfrac{B}{p^{p}}$$
The substances having very short plastic region are
  • Ductile
  • Brittle
  • Malleable
  • All of these
A neutron moving with a velocity $$v$$ and kinetic energy $$E$$ collides perfectly elastically head on with the nucleus of an atom of mass number $$A$$ at rest. The energy received by the nucleus and the total energy of the system are related by
  • $$\cfrac { 4A }{ { \left( A+1 \right) }^{ 2 } } $$
  • $${ \left( \cfrac { A-1 }{ A+1 } \right) }^{ 2 }$$
  • $$\cfrac{(A+1)}{4{A}^{2}}$$
  • $${ \left( \cfrac { A+1 }{ A-1 } \right) }^{ 2 }$$
When a $$20g$$ mass hangs attached to one end of a light spring of length $$10cm$$, the spring stretches by $$2cm$$. The mass is pulled down unitl the total length of the spring is $$14cm$$. The elastic energy, in Joule stored in the spring is -
  • $$4\times {10}^{-2}$$
  • $$4\times {10}^{-3}$$
  • $$8\times {10}^{-2}$$
  • $$8\times {10}^{-3}$$
One end of a uniform rod of mass $$M$$ and cross-sectional area $$A$$ is suspended from the other end. The stress at the mid-point of the rod will be :
  • $$ \dfrac {2Mg}{A}$$
  • $$ \dfrac {3Mg}{2A}$$
  • $$ \dfrac {Mg}{A}$$
  • Zero
A force $$F$$ is applied along a rod of transverse sectional area $$A$$. The normal stress to a sectior $$PQ$$ inclined $$\theta$$ to transverse section will be maximum for $$\theta$$ (in degree) is 
1125154_80de3fc4109b43bfa7d8056376bc8ed7.png
  • $$0$$
  • $$30$$
  • $$45$$
  • $$90$$
A steel wire of length $$1.5\ m$$ and area of cross section $$1.5\ mm^{2}$$ is stretched by $$1.5\ cm$$. then the work done per unit volume. $$(Y =2\times 10^{11}Nm^{2})$$.
  • $$1\times 10^{7}J/m^{3}$$
  • $$2\times 10^{7}J/m^{3}$$
  • $$3\times 10^{7}J/m^{3}$$
  • $$4\times 10^{7}J/m^{3}$$

A thick rope of rubber of density $$1.5 \times {10^3}{\text{kg/}}{{\text{m}}^{\text{3}}}$$ and Young's modulus $$5 \times {10^6}{\text{N/}}{{\text{m}}^2}$$ , $$8 m$$ length is hung from the ceiling of a room , the increases in its length due to its own weight is :

 $$\left( {g = 10{\text{m/}}{{\text{s}}^{\text{2}}}} \right)$$
  • $$9.6 \times {10^{{\text{ - 2}}}}{\text{m}}$$
  • $$19.2 \times {10^{{\text{ - 7}}}}{\text{m}}$$
  • $$9.6 \times {10^{{\text{ - 7}}}}{\text{m}}$$
  • $$9.6 m$$
The average density of Earth's crust $$10km$$ benearth the surface is $$2.7gm/cm^3$$. The speed of longitudinal seismic waves at that depth is $$5.4km/s$$. The bulk modulus of Earth's crustconsidering its behaviour aas fluid at that depth is:
  • $$7.9\times 10^{10}Pa$$
  • $$5.6\times 10^{10}Pa$$
  • $$7.9\times 10^{7}Pa$$
  • $$1.46\times 10^{7}Pa$$
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 
1152580_b60fcab9ae9c4125946cf246ed0041fe.png
  • $$\dfrac { 3{ W }^{ 2 }L }{ 4\pi { R }^{ 2 }Y }$$
  • $$\dfrac { 3{ W }^{ 2 }L }{ 8\pi { R }^{ 2 }Y }$$
  • $$\dfrac { 5{ W }^{ 2 }L }{ 8\pi { R }^{ 2 }Y }$$
  • $$\dfrac { { W }^{ 2 }L }{ \pi { R }^{ 2 }Y } $$
What is the approximate change in density of water in a lake at a depth of 400 m below the surface? The density of water at the surface is 1030 kg/$${m^3}$$ and bulk modulus of water is $$2 \times {10^9}N/{m^3}$$
  • 4 kg/$${m^3}$$
  • 2 kg/$${m^3}$$
  • 6 kg/$${m^3}$$
  • 8 kg/$${m^3}$$
Assume that a block of very low shear modulus is fixed on an inclined place as shown. Due to elastic forces it will deform. What will be the shape of the block?
1177024_192019c022d5496c9a57b27b6f90facd.png
  • none 
  • all of these
A material has normal density $$\rho$$ and bulk modulus $$B$$. The increase in the density of the material, when it is subjected to an external pressure $$P$$ from all sides is :
  • $$\cfrac { P }{ \rho B } $$
  • $$\cfrac { BP }{ \rho } $$
  • $$\cfrac { P \rho }{ B } $$
  • $$\cfrac { B \rho }{ P } $$
A horizontal rod is supported at both ends and loaded at the middle. It L and Y are length and Young's modulus respectively, then depression at the middle is directly proportional to
  • L
  • $${ L }^{ 2 }$$
  • Y
  • $$\dfrac { 1 }{ Y } $$
A-3 Two wire of equal length and cross-sectional area suspended as shown in figure. Their Young's modulus are $$ Y_1 and Y_2 $$ respectively. The equivelent Young's modulus will be 
1232407_a5287fe924f64bf4b16f4b3a61ca4d35.png
  • $$ Y_1 + Y_2 $$
  • $$ \frac { Y_ 1+Y_ 2 }{ 2 } $$
  • $$ \frac { Y_ 1Y_ 2 }{ Y_1 + Y_2 } $$
  • $$ \sqrt { Y_ 1Y_ 2 } $$
If a rubber ball is taken down to a 100 m deep lake, its volume decreases by 0.1%. If $$g=10\quad m/{ s }^{ 2 }$$ then the bulk modulus of elasticity for rubber, in N/$${ m }^{ 2 }$$, is 
  • $${ 10 }^{ 8 }$$
  • $${ 10 }^{ 9 }$$
  • $${ 10 }^{ 11 }$$
  • $${ 10 }^{ 10 }$$
A $$2\ m$$ long light metal rod $$AB$$ is suspended from the ceiling horizontally by means of two vertical wires of equal length, tied to its ends. One wire is of brass and has cross-section of $$0.2 \times 10 ^ { - 4 }\ m ^ { 2 }$$ and the other is of steel with $$0.1 \times 10 ^ { 4 }\ m^2$$ cross-section. In order to have equal stresses in the two wires, a weight should be hung from the rod from end $$A$$ a distance of
1217679_f4c4b7c328074b3aa85bbb374847dd5d.png
  • $$66.6\ cm$$
  • $$133\ cm$$
  • $$44.4\ cm$$
  • $$155.6\ cm$$
A particle of mass $$m$$ is moving with constant speed $$v$$ in a circular path on a smooth horizontal plane by a spring as shown. If the natural length of the spring is $$l _ 0$$ and stiffness of the spring is $$k$$, the elongation of the spring is :
1210187_c224823f775c44c897fb679e64ba64e3.png
  • $$\dfrac { { k }^{ 2 }{ l }_{ 0 }^{ 2 }+4{ mv }^{ 2 }{ k }-{ kl }_{ 0 } }{ 2k } $$
  • $$\dfrac { \sqrt { { k }^{ 2 }{ l }_{ 0 }^{ 2 }+{ 4mv }^{ 2 }k } -{ kl }_{ 0 } }{ 2k } $$
  • $$\dfrac { \sqrt { { k }^{ 2 }{ l }_{ 0 }^{ 2 }+{ 4mv }^{ 2 }k-{ kl }_{ 0 } } }{ 2k } $$
  • $$\dfrac { \sqrt { { k }^{ 2 }{ l }_{ 0 }^{ 2 }+{ 4mv }^{ 2 }k } +{ kl }_{ 0 } }{ 2k } $$
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 
  • $$\dfrac { 3{ W }^{ 2 }L }{ 4\pi { R }^{ 2 }Y }$$
  • $$\dfrac { 3{ W }^{ 2 }L }{ 8\pi { R }^{ 2 }Y }$$
  • $$\dfrac { 5{ W }^{ 2 }L }{ 8\pi { R }^{ 2 }Y }$$
  • $$\dfrac { { W }^{ 2 }L }{ \pi { R }^{ 2 }Y } $$
The intensity at the maximum in a Young's double slit experiment is $${ I }_{ 0 }$$. Distance between two slits is $$d=5\lambda $$, where $$\lambda $$ is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen at a distance $$D = 10 d$$ ?
  • $${ I }_{ 0 }$$
  • $$\cfrac { { I }_{ 0 } }{ 4 } $$
  • $$\cfrac { 3 }{ 4 } { I }_{ 0 }$$
  • $$\cfrac { { I }_{ 0 } }{ 2 } $$
Find the stress in $$CD.$$
Area of $$CD = 2\ m^2$$
1217670_d775744f8703447cacd5a75c30f62fbe.png
  • $$15\ N/m^2$$
  • $$5\ N/m^2$$
  • $$20\ N/m^2$$
  • $$None \ of  \ these$$
The increase in length of a wire is$$ \Delta \ell $$ when force 'F' is applied on one end of the wire with its other end fixed with a rigid support. Ratio of energy stored in the wire to the work done in stretching it is
  • 1:1
  • 2:1
  • 1:2
  • 1:4
A uniform steel wire hangs from the ceiling and elongates due to its own weight. The ratio of elongation of the lower half of wire is 
  • 4:1
  • 3:1
  • 3:2
  • 1:1
A wire is stretched by 0.01 m by a certain force 'F' another wire of  same material whose diameter and lengths are double to original wire is stretched b the same force then its elongation will be-
  • 0.005 m
  • 0.01m
  • 0.02 m
  • 0.04 m
When a temperature of a gas is $$20^0C$$ and pressure is changed from $$P_1 = 1.01 \times 10^5$$ Pa to $$P_2 = 1.165 \times 10^5$$ Pa then the volume changed by 10%. The bulk modulus is
  • $$1.55 \times 10^5$$ Pa
  • $$0.115 \times 10^5$$ Pa
  • $$1.4 \times 10^5$$ Pa
  • $$1.01 \times 10^5$$ Pa
A wire of length $$1\, m$$ and its area of cross-section is $$1\, cm^3$$. The Young's modulus of the wire is $$10^{11}\, Nm^{-2}$$. Two forces each equal to $$F$$ are applied on its two ends in the opposite directions. If the change in length be $$1\, mm$$, what is the value of $$F$$?
  • $$0.5 \times 10^4 \, N$$
  • $$10^4 \, N$$
  • $$2 \times 10^4 \, N$$
  • None of these

A massless and thin string is wrapped several times around a disc kept on a rough horizontal surface. A boy standing at a distance 'd' for the cylinder holds free end of the string pulls the cylinder towards him. If there is no slipping, length of the string passed through the hand of the boy while the cylinder reaches his hands is
  • $$d$$
  • $$2d$$
  • $$3d$$
  • $$4d$$
One end of a uniform wire of length Land of weight Wis attached rigidly to a point in the roof and a weight $$W_1$$, is suspended from its lower end. If $$A$$ is the area of cross section of the wire, the stress in the wire at a height $$\cfrac{6L}{8}$$ from its lower end is
  • $$\cfrac{W_1}{A}$$
  • $$\cfrac{W_1+(W/4)}{A}$$
  • $$\cfrac{W_1+(3W/4)}{A}$$
  • $$\cfrac{W_1+W}{A}$$
Y,K,n represent the Young's modulus, bulk modulus and rigidity modulus of a body respectively. If rigidity modulus is twice the bulk modulus, then 
  • $$Y=5K/18$$
  • $$Y=5 n/9$$
  • $$Y=9K/5$$
  • $$Y=18K/5$$

 An elastic string carrying a body of mass 'm' extends by 'e'. The body rotates in a vertical circle with critical velocity. The extension in the string at the lowest position is 
  • $$2$$ e
  • $$4$$ e
  • $$6$$ e
  • $$8$$ e
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,):
  • $${ sin }^{ -1 }\left( { 0.33\times 10 }^{ 8 } \right) $$
  • $${ sin }^{ -1 }\left( { 0.33\times 10 }^{ 6 } \right) $$
  • $${ sin }^{ -1 }\left( { 3\times 10 }^{ 8 } \right) $$
  • $${ sin }^{ -1 }\left( { 3\times 10 }^{ -6 } \right) $$
A rod of length $$L$$ with square cross-section $$(a \times a)$$ is bend to form a circular ring.
Then the value of stress developed at points $$E$$ and $$F$$ respectively, ($$Y$$ is Young's modulus of metal rod)

1324119_d9d5c1c4d031457889db9e2ccc3ec7f0.PNG
  • Zero in both
  • $$\dfrac{2\pi a Y}{L}$$ compression, $$\dfrac{2\pi a Y}{L}$$ tension
  • $$\dfrac{\pi a Y}{L}$$ compression, $$\dfrac{\pi a Y}{L}$$ tension
  • $$2\dfrac{\pi a Y}{L}$$ compression in both.
A uniform slender rod of length L, cross-sectional area A and Young's modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is
1327387_267085780dfb4ca1b16dadbb36600422.png
  • $$\dfrac{3FL}{5AY}$$
  • $$\dfrac{2FL}{5AY}$$
  • $$\dfrac{3FL}{8AY}$$
  • $$\dfrac{8FL}{3AY}$$
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