CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 9 - MCQExams.com

Select the correct alternative(s).
  • Elastic forces are always conservative
  • Elastic forces are not always conservative
  • Elastic forces are conservative only when Hooke's law is obeyed
  • Elastic forces may be conservative even when Hooke's law is not obeyed
When the load on a wire is increasing slowly from $$2$$ kg to $$4$$ kg, the elongation increases from $$0.6$$ mm to $$1$$ mm. The work done during this extension of the wire is $$(g=10 m/s^2)$$.
  • $$14\times 10^{-3}$$J
  • $$0.4\times 10^{-3}$$J
  • $$8\times 10^{-2}$$J
  • $$10^{-3}$$J
What is the percentage increase in length of a wire of diamater $$2.5\ mm$$, stretched by  a force of $$100\ Kg\ wt$$? Youngs modulus of elasticity of wire $$=1.25 \times {10}^{11}\ dyne/{cm}^{2}$$
  • $$0.16\%$$
  • $$0.32\%$$
  • $$0.08\%$$
  • $$0.12\%$$
A steel wire has length 2.0  m, radius 1 mm and $$Y = 2 \times 10^{11} N/m^2$$ A sphere of mass 1 kg is attached at one end of the wire which is then whirled in a vertical circle with speed 2 rev/sec. Elongation of the wire when mass is at the lowest position. 
  • 1.0 mm
  • 2.0 mm
  • 0.1 mm
  • 0.01 mm
Two copper wires having the length in ratio $$4:1$$ and their radii ratio as $$1:4$$ are stretched by the same force. Then the ratio of the longitudinal strain in the two will be 
  • $$1:16$$
  • $$16:1$$
  • $$1:64$$
  • $$64:1$$
A block of mass of $$2kg$$ is attached to one end of a wire of cross sectional area $$1mm \,\,\,2 $$ and is. Find the elongation of the wire when the block is at top of the circle $$(Y=2\times 10^{11}Nm^{-2})$$
  • $$0.2892 mm$$
  • $$0.054 mm$$
  • $$01446 mm$$
  • $$0.0017 mm$$
Scalar are quantity that are describe by 
  • Direction
  • Magnitude and direction 
  • Magnitude
  • Motion
A wire of density $$9\times{10^3}kg/{m^3}$$ is stretched between two clamps 1 m apart and is stretched to an extension of $$4.9\times{10^{ - 4}}metre.$$ Young's modulus of material is $$9\times{10^{10}}N/{m^2}$$. Then
  • The lowest frequency of standing wave is 35 Hz
  • The frequency of 1st overtone is 70 Hz
  • The frequency of 1st overtone is 105 Hz
  • The stress in the wire is $$4.41\times{10^7}N/{m^2}$$
A two meter long rod is suspended with the help of two wires of equal length. One wire is of steel and its cross-section is 0.1 $$cm^{2} $$ and another wire is of brass and its cross-section area is 0.2 $$cm^{2} $$. If a load W is suspended from the rod and introduced in both the wires is same then the ratio of tensions in them will be
1030671_51e9441439664f22adb094f9faf1a702.png
  • (a) will depend on the position of W
  • (b) $$T_{1}/T_{2}=2$$
  • (c) $$T_{1}/T_{2}=1$$
  • (d) $$T_{1}/T_{2}=0.5$$
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 dyne $${cm}^{-2}$$ is:
  • $$10\times {10}^{11}$$
  • $$100\times {10}^{2}$$
  • $$1\times {10}^{11}$$
  • $$2\times {10}^{11}$$
The length of of a metal wire $$l$$ when the tension in is $$'F'$$ and $$'xl'$$ when the tension is $$'yF'$$. Then the natural length of the wire is 
  • $$\dfrac { \left( x-y \right) l }{ x-1 } $$
  • $$\dfrac { \left( y-x \right) l }{ y-1 } $$
  • $$\dfrac { \left( x-y \right) l }{ x+1 } $$
  • $$\dfrac { \left( y-x \right) l }{ y+1 } $$
A tungsten wire of length 20 cm is stretched by 0.1 cm. Find the strain on the wire.
  • 0.002
  • 0.005
  • 0.001
  • 0.004
When temperature of a gas is $$20^oC$$ and pressure is changed from $${ P }_{ 1 }=1.0\times { 10 }^{ 5 } Pa$$ to $${ P }_{ 2 }=1.65\times { 10 }^{ 5 } Pa$$ and the volume is changed by 10%. The bulk modulus is :
  • $$1.55\times { 10 }^{ 5 }Pa$$
  • $$1.15\times { 10 }^{ 5 }Pa$$
  • $$1.4\times { 10 }^{ 5 }Pa$$
  • $$1.01\times { 10 }^{ 5 }Pa$$
A solid cube is subjected to a pressure of $$\left( 5\times { 10 }^{ 5 }\quad N/{ m }^{ 2 } \right) $$. Each side of the cube is shortened by then volumetric strain and Bulk modulus of the cube are
  • $$0.03,5\times { 10 }^{ 5 }\quad N/{ m }^{ 2 }$$
  • $$0.03,1.67\times { 10 }^{ 7 }\quad N/{ m }^{ 2 }$$
  • $$3,1.67\times { 10 }^{ -7 }\quad N/{ m }^{ 2 }$$
  • $$0.01,1.67\times { 10 }^{ 7 }\quad N/{ m }^{ 2 }$$
Three wires P,Q and R the same materials and length have radii $$0.12cm,0.2cm$$ and $$0.3cm$$ respectively. Which wire has the highest value of Young's modules of elasticity ?
  • P
  • Q
  • R
  • All have the same value
The stress required to double the length of wire (or) to produce $$100\%$$ longitudinal strain is:
  • $$Y$$
  • $$\cfrac{Y}{2}$$
  • $$2Y$$
  • $$3Y$$
 A uniform rod of length $$60 cm$$ and mass $$6kg$$ is acted upon by two forces as shown in the diagram. The force exerted by $$45 cm$$ part of the rod on $$15 cm$$ part of the rod is 

1069048_d060a9f94f934fcba734703899e8a40e.JPG
  • $$9 N $$
  • $$ 18 N $$
  • $$27 N $$
  • $$30 N $$
Two wires A and B are identical in shape and size are stretched by same magnitude of force. Then the extensions are found to be 0.2% and 0.3% respectively. Find the rate of their Young's modulii
  • 2 : 3
  • 3 : 2
  • 4 : 9
  • 9 : 4
For a material $$Y={ 6.6\times 10 }^{ 10 }\ { N/m }^{ 2 }$$ and bulk modulus $$K{ 11\times 10 }^{ 10 }\ { N/m }^{ 2 }$$, then its Poisson's ratio is:
  • $$0.8$$
  • $$0.35$$
  • $$0.7$$
  • $$0.4$$
A copper wire and an aluminium wire have lengths in the ratio 3:2, diameters in the ration 2:3 and forces applied in the ration 4:Find the ratio of the increase in the length of the two wires. 
$$\left( { Y }_{ cu }=1.1\times { 10 }^{ 11 }N{ m }^{ -2 },\quad { Y }_{ Al }=0.70\times { 10 }^{ 11 }N{ m }^{ -2 }\quad  \right) $$
  • 110:189
  • 180:110
  • 189:110
  • 80:11
In the Searle's method to determine the Young's modulus of a wire, a steel wire of length $$156\ cm$$ and diameter $$0.054\ cm$$ is taken as experimental wire. The average increase in length for $$1.5\ kg\ wt$$ is found to be $$0.050\ cm$$. Then the Young's modulus of the wire is
  • $$3.002\times 10^{11}N/m^{2}$$
  • $$1.002\times 10^{11}N/m^{2}$$
  • $$2.002\times 10^{11}N/m^{2}$$
  • $$2.5\times 10^{11}N/m^{2}$$
Three bars having length $$l,2l$$ and $$3l$$ and area of cross-section $$A,2A$$ and $$3A$$ are joined rigidly and to end. Compound rod is subjected to a stretching force $$F$$. The increase in length of rod is (Young's modulles of material is $$Y$$ and bars are massless)
  • $$\dfrac {13Fl}{2\ AY}$$
  • $$\dfrac {3Fl}{AY}$$
  • $$\dfrac {9Fl}{AY}$$
  • $$\dfrac {13\ Fl}{AY}$$
A hydraullic press contains $$250 lit$$ of oil. Find the decrease in volume of the oil when its  pressure increases to $$ 10^7 Pa$$ . The bulk modulus of the oil is $$ K = 5 \times 10^5 Pa$$
  • $$- 0.8 lit$$
  • $$- 0.5 lit$$
  • $$- 0.6 lit$$
  • $$- 0.9 lit$$
The breaking stress of aluminium is $$7.5\times 10^{7}Nm^{-2}$$. The greatest length of aluminium wire that can hang vertically without breaking is(Density of auminium is $$2.7\times 10^{3}\ kg\ m^{-3}$$)
  • $$283\times 10^{3}\ m$$
  • $$28.3\times 10^{3}\ m$$
  • $$2.83\times 10^{3}\ m$$
  • $$0.283\times 10^{3}\ m$$
A uniform rod of mass m and length $$l$$ is rotating with constant angular velocity $$\omega$$ about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :
  • $$\dfrac{m\omega^2l}{8AY}$$
  • $$\dfrac{3m\omega^2l}{8AY}$$
  • $$\dfrac{3m\omega^2l}{4AY}$$
  • $$\dfrac{m\omega^2l}{4AY}$$
The length of a rubber cord is $$l_1$$ metres when the tension in it is $$4N$$ and $$l_2$$ metres when the tension is $$5N$$. then the length in meters when the tension is $$9N$$ is
  • $$3l_2 +4l_1$$
  • $$3l_2 +2l_1$$
  • $$5l_2 - 4l_1$$
  • $$3l_2 - 2l_1$$
The extension of wire by application of load is $$0.3cm$$  The extension in a w wire of same material but of double the length and half the radius of cross section by the same load will be in (cm) 
  • $$0.3$$
  • $$0.6$$
  • $$0.2$$
  • $$2.4$$
An aluminium rod has a breaking strain $$0.2\%$$. The minimum cross-sectional area of the rod in $$m^{2}$$ in order to support a load of $$10^{4}N$$ is if (Young's modulus is $$7\times 10^{9}Nm^{-2}$$)
  • $$1.7\times 10^{-4}$$
  • $$1.7\times 10^{-3}$$
  • $$7.1\times 10^{-4}$$
  • $$1.4\times 10^{-4}$$
Two wires A and B have young's modulii in the ratio $$1:2$$ and ratio of the lengths is $$1:1$$. under the application of same stress the ratio of elongation is
  • $$1:1$$
  • $$1:2$$
  • $$2:1$$
  • $$1:4$$
A steel wire $$2\ m$$ in length is stretched by $$1\ mm$$. The cross-sectional area of the wire is $$2\ mm^{2}$$. If Young's modulus of steel is $$2\times 10^{11}\ N/m^{2}$$, then the elastic potential energy stored in the wire is
  • $$0.1\ J$$
  • $$0.2\ J$$
  • $$0.3\ J$$
  • $$0.4\ J$$
An aluminium wire and a steel wire of the same length and cross-section joined end to end. The composite wire is hung from a rigid support and a load is suspended from the free end. If the increase in the length of $$t\ h\ c$$ composite wire is $$2.7\ mm$$, then the increase in the length of each wire is (in $$mm$$).$$(Y_{At}=2\times 10^{11}Nm^{-3}, Y_{steel}=7\times 10^{11}Nm^{-2})$$
  • $$1, 7, 1$$
  • $$1.3, 1, 4$$
  • $$1.5, 1, 2$$
  • $$2.1, 1, 0.6$$
Consider the bar in Fig. Cross-sectional area $$A_{e} = 1.2 in.^{2}$$, and Young's modulus $$E = 30\times 10^{6} psi$$. If $$q_{1} = 0.02\ in.$$ and $$q_{2} = 0.025\ in.$$, determine the following (by hand calculation).
  • The displacement at point $$P$$
  • The strain $$\epsilon$$ and stress $$\sigma$$
  • The element stiffness matrix, and
  • The strain energy in the element
The force constant of a wire is $$k$$ and that of another wire of the same material is $$2k$$. When both the wires are stretched, then work done is
  • $$W_{2}=1.5W_{1}$$
  • $$W_{2}=2W_{1}$$
  • $$W_{2}=W_{1}$$
  • $$W_{2}=0.5W_{1}$$
A uniform cubical block is subjected to volumetric compression, which decreases its each side of $$2$$%. The Bulk strain produced in it is:
  • $$0.03$$
  • $$0.02$$
  • $$0.06$$
  • $$0.12$$
There are two wires of same material. their radii and lengths are both in the ratio 1:if the extensions produced are equal, what is the ratio of the loads?
  • 1:2
  • 2:1
  • 1:4
  • 4:1
A thick rope of density $$\rho$$ and length $$L$$ is hung from a rigid support. The Young's modulus of the material of rope is $$Y$$. The increase in length of the rope due to its own weight is
  • $$\rho g{L}^{2}/4Y$$
  • $$\rho g{L}^{2}/2Y$$
  • $$\rho g{L}^{2}/Y$$
  • $$\rho gL/Y$$
When a wire is stretched, its length increases by 0.3% and the diameter decreases by 0.1%. Poisson's ratio of the material of the wire is about
  • 0.03
  • 0.333
  • 0.15
  • 0.015
A steel ring of radius $$r$$ and cross sectional area $$A$$ is fitted on to a wooden disc of radius $$R(R> r)$$. If Young;s modulus be $$Y$$, then the force with which the steel ring is expanded, is
  • $$AY\cfrac{R}{r}$$
  • $$AY(\cfrac{R-r}{r})$$
  • $$\cfrac{Y}{A}\cfrac{(R-r)}{r}$$
  • $$\cfrac{Yr}{AR}$$
Volume of a liquid when compressed by additional pressure of $$10^5 N/m^2$$ is $$196$$cc and when compressed by a pressure of $$1.5 \times 10 ^5 N/m^2$$, the volume is $$194cc$$. The bulk modulus of the liquid is:
  • $$10^5N/m^2$$
  • $$1.5 \times 10^6$$
  • $$5 \times10^5N/m^2$$
  • $$5 \times 10^6N/m^2$$
The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will 
  • be double
  • be half
  • be four times
  • remain same
One end of a uniform wire of length L and of weight W you is attached rigidly see through a point in the roof and weight W1 is suspended from its lower end. If S is true area of cross section of the wire the stress in the wire at a height (3L/4) from its lower end is :
  • $$[W_1 + (W/4)] / S$$
  • $$W_1/S$$
  • $$[W_1 + (3W/4)] / S$$
  • $$(W_1+W) / S$$
A uniform rod of length $$L$$ has a mass per unit length $$\lambda$$ and area of cross section $$A$$. If the Young's modulus of the rod is $$Y$$. The elongation in the rod due to its own weight is
  • $$\dfrac{2\lambda gL^2}{AY}$$
  • $$\dfrac{\lambda gL^2}{2AY}$$
  • $$\dfrac{\lambda gL^2}{4 AY}$$
  • $$\dfrac{\lambda gL^2}{6AY}$$
The relationship between Young's modulus $$Y$$, Bulk modulus $$K$$ and modulus of rigidity $$\eta$$ is:-
  • $$Y = \dfrac{9 \eta K}{3 + k}$$
  • $$Y = \dfrac{9 \eta K}{n + 3}$$
  • $$Y=\dfrac{9 \eta K}{\eta+3 k}$$
  • $$Y = \dfrac{3 \eta K}{9 \eta + k}$$
Two wires of same material and radius have their lengths in ratio $$1:2$$. If these wires are stretched by the same force, the strain produced in the two wires will be in the ratio
  • $$2:1$$
  • $$1:1$$
  • $$1:2$$
  • $$1:4$$
A rod of mass $$'M'$$ is subjected to force $$'t'$$ and $$'2f'$$ at both the ends as shown in the figure. If young modulus of its material is $$'y'$$ and its length is $$L$$ find total elongation of rod.
1136358_9c97aad0427d4c3bbb0060bf21b9d8bd.png
  • $$\dfrac{fl}{2Ay}$$
  • $$\dfrac{fl}{Ay}$$
  • $$\dfrac{3fl}{2Ay}$$
  • $$\dfrac{4fl}{2Ay}$$
The bulk modulus of water is $$2.1 \times 10^9 N/m^2$$. The pressure required to increase the density of water by $$0.1$$% is:-
  • $$2.1 \times 10^5 N/m^2$$
  • $$2.1 \times 10^3 N/m^2$$
  • $$2.1 \times 10^6 N/m^2$$
  • $$2.1 \times 10^7 N/m^2$$
A wire is stretched by $$0.01\ m$$ by a certain force $$F$$. Another wire of same material whose diameter and lengths are doubled to the original wire is stretched by the same force. Then its elongation will be:
  • $$0.005\ m$$
  • $$0.01\ m$$
  • $$0.02\ m$$
  • $$0.08\ m$$
If the temperature of a wire of length $$2m$$ area of cross-section $$1{cm}^2$$ is increased from $${0^ \circ}C$$ to $${80^ \circ}C$$ and is not allowed to increase in length, then force required for it is {$$Y = 10^{10}N/m^2, \alpha = 10^{ - 6}/^oC$$}
  • $$80N$$
  • $$160N$$
  • $$400N$$
  • $$120N$$
The pressure of a medium is changed from $$1.01\times 10^{5}\ Pa$$ to $$1.165\times 10^{5}\ Pa$$ and change in volume is $$10\%$$ keeping temperature constant. The bulk modulus of the medium is 
  • $$204.8\times 10^{5}\ Pa$$
  • $$102.4\times 10^{5}\ Pa$$
  • $$51.2\times 10^{5}\ Pa$$
  • $$1.55\times 10^{5}\ Pa$$
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 $$Y=1.2\times 10^{11}Nm^{-2}$$ 
  • $$6\times 10^4J$$
  • $$6\times 10^{-3}J$$
  • $$6\times 10^{3}J$$
  • $$6\times 10^{-4}J$$
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