CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 6 - MCQExams.com

Two wires of the same material and length but diameters in ratio $$1:2$$ are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio :-
  • $$16 :1$$
  • $$4:1$$
  • $$2:1$$
  • $$1:1$$
The graph showing the extension of is wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. of the cross-sectional area of the wire is $$1{mm}^{2}$$, then the Young's modulus of the material  of the wire .( In graph, X-axis 1 unit =  10mm)  .
289752.png
  • $$2\times {10}^{11}N{m}^{-1}$$
  • $$2\times {10}^{10}N{m}^{-2}$$
  • $$\dfrac {1}{2}\times {10}^{11}N{m}^{-2}$$
  • None of these
Copper wire of length $$3m$$ and area of cross-section $$1\:mm^{2}$$, passes through an arrangement of two frictionless pulleys, $$P_{1}$$ and $$P_{2}$$. One end of the wire is rigidly clamped and a mass of $$1 kg$$ is hanged from the other end. If Young's modulus for copper is $$10\times 10^{10}N/m^{2}$$, the elongation in the wire is :

282783_2a7f78b5a04546608c330f0aa26465ba.png
  • $$0.05 mm$$
  • $$0.1 mm$$
  • $$0.2 mm$$
  • $$0.3 mm$$
An increase in pressure required to decreases the $$100\  liters$$ volume of a liquid by $$0.004$$% in container is: (Bulk modulus of the liquid $$=2100\:MPa$$):
  • $$188\  kPa$$
  • $$8.4\  kPa$$
  • $$18.8 \ kPa$$
  • $$84 \ kPa$$
A ball falling in a lake of depth 200 m show 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball:-
  • $$19.6\times 10^{8}N/m^{2}$$
  • $$19.6\times 10^{-10}N/m^{2}$$
  • $$19.6\times 10^{10}N/m^{2}$$
  • $$19.6\times 10^{-8}N/m^{2}$$
A steel wire $$1.5 m$$ long and of radius $$1 mm$$ is attached with a load $$3 kg$$ at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency $$2Hz$$. Find the elongation of the wire when the weight is at the lowest position:
($$Y=2\times 10^{11}N/m^{2}$$ and $$g=10\:m/s^{2}$$)
  • $$1.77\times 10^{-3}m$$
  • $$7.17\times 10^{-3}m$$
  • $$3.17\times 10^{-7}m$$
  • $$1.37\times 10^{-7}m$$
There is no change in the volume of a wire due to change in its length on stretching. The Poisson's  ratio of the material of the wire is :
  • $$+0.50$$
  • $$-0.50$$
  • $$0.25$$
  • $$-0.25$$
A copper wire having $$Y=1\times 10^{11}N/m^{2}$$ with length $$6m$$ and a steel wire having $$Y=2\times 10^{11}N/m^{2}$$ with  length $$4 m$$ each of cross section $$10^{-5}m^{2}$$ are fastened end to end stretched by a tension of $$100 N$$. The elongation produced in the copper wire is :
  • $$0.2 mm$$
  • $$0.4 mm$$
  • $$0.6 mm$$
  • $$0.8 mm$$
The bulk modulus of rubber is $$9.8\times 10^{8}N/m^{2}$$. To what depth a rubber ball be taken in a lake so that its volume is decreased by $$0.1$$% ?
  • $$1 km$$
  • $$25 km$$
  • $$100 km$$
  • $$200 km$$
When a force is applied on a wire of uniform cross-sectional area $$3\times 10^{-6}m^{2}$$ and length $$4 m$$, the increase in length is $$1\ mm$$. Energy stored in it will be ($$Y=2\times 10^{11}N/m^{2}$$):
  • $$6250\  J$$
  • $$0.177\  J$$
  • $$0.075\  J$$
  • $$0.150\  J$$
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
  • $$\displaystyle 10^{8}$$
  • $$\displaystyle 2\times 10^{8}$$
  • $$\displaystyle 10^{9}$$
  • $$\displaystyle 2\times 10^{9}$$
If the potential energy of a spring is V on stretching it by 2 cm then its potential energy when it is stretched by 10 cm will be
  • V/25
  • 5 V
  • V/5
  • 25 V
If the ratio of lengths, radii and Youngs modulii of steel and brass wires in the figure are a, b and c respectively. Then the corresponding ratio of increase in their lengths would be:
293473_4de9a8f7e3ff4cf992e6b6a15b3e36cf.png
  • $$\displaystyle \dfrac{2ac}{b^{2}} $$
  • $$\displaystyle \dfrac{3a}{2b^{2}c} $$
  • $$\displaystyle \dfrac{3c}{2ab^{2}} $$
  • $$\displaystyle \dfrac{2a^{2}c}{b} $$
A force F is needed to break a copper wire having radius R The force needed to break a copper wire of radius 2R will be
[assume F is applied along the wire and the wire obeys Hooke's law until it breakes]
  • F/2
  • 2 F
  • 4 F
  • F/4
Two wires of equal length and cross section area suspended as shown in figure. Their Youngs modulus are $$\displaystyle Y_{1}\: \: and\: \: Y_{2}$$ respectively The equivalent Youngs modulus will be 
293290_d2951b68963b442ea6bdc3092979766c.png
  • $$\displaystyle Y_{1}+ Y_{2}$$
  • $$\displaystyle \frac{Y_{1}+Y_{2}}{2}$$
  • $$\displaystyle \frac{Y_{1}Y_{2}}{Y_{1}+Y_{2}}$$
  • $$\displaystyle \sqrt{Y_{1}Y_{2}}$$
A metal block is experiencing an atmospheric pressure of $$\displaystyle 1\times 10^{5}N/m^{2}$$ when the same block is placed in a vaccum chamber the fractional change in its volume is (the bulk modulus of metal is $$\displaystyle 1.25\times 10^{11}N/m^{2}$$) 
  • $$\displaystyle 4\times 10^{-7}$$
  • $$\displaystyle 2\times 10^{-7}$$
  • $$\displaystyle 8\times 10^{-7}$$
  • $$\displaystyle 1\times 10^{-7}$$
The high domes of ancient buildings have structural value (besides beauty). It arises from pressure difference on the two faces due to curvature (as in soap bubbles). There is a dome of radius 5 m and uniform (but small) thickness. The surface tension of its masonry structure is about 500 N/m. Treated as hemispherical, the maximum load the dome can support is nearest to 
  • 1500 kg wt.
  • 3000 kg wt.
  • 6000 kg wt.
  • 12000 kg wt.
The diameter of a brass rod is $$4mm$$ and Youngs modulus of brass is $$\displaystyle 9\times 10^{10}N/m^{2}$$ The force required to stretch it by $$0.1\%$$ of its length is
  • $$\displaystyle 360\pi N$$
  • $$36 N$$
  • $$\displaystyle 144\pi \times10^{3} N$$
  • $$\displaystyle 36\pi \times10^{5} N$$
Two wires of the same material and length but diameter in the ratio 1 : 2 are stretched by the same force. The ratio of potential energy per unit volume for the two wires when stretched will be :
  • 1 : 1
  • 2 : 1
  • 4 : 1
  • 16 : 1
One end of a uniform rope of length L and of weight w is attached rigidIy to a point in the roof and a weight w$$_1$$ is suspended from its lower. If s is the area of cross-section of the wire, the stress in the wire at a height $$\displaystyle \frac{3 L}{4}$$ from its lower end is:
  • $$\displaystyle \frac{w}{s}$$
  • $$\displaystyle \frac{\displaystyle w_1 + \frac{w}{4}}{s}$$
  • $$\displaystyle \frac{\displaystyle w_1 + \frac{2w}{4}}{s}$$
  • $$\displaystyle \frac{\displaystyle w_1 + w}{s}$$
With what minimum acceleration can a fireman slide down a rope whose breaking strength is 3/4 th of his weight ? 
  • 1/4 g
  • 1/2 g
  • 3/4 g
  • zero
Assertion: Stress is the internal force per unit area of a body. 
Reason: Rubber is more elastic than stee
  • If both assertion and reason are true but the reason is the correct explanation of assertion.
  • If both assertion and reason are true but the reason is not the correct explanation of assertion.
  • If assertion is true but reason is false.
  • If both the assertion and reason are false.
  • If reason is true but assertion is false.
If in a wire of Young's modulus Y, longitudinal strain X is produced then the potential energy stored in its unit volume will be : 
  • $$\displaystyle 0.5Y{ X }^{ 2 }$$
  • $$\displaystyle 0.5{ Y }^{ 2 }X$$
  • $$\displaystyle 2Y{ X }^{ 2 }$$
  • $$\displaystyle Y{ X }^{ 2 }$$
If $$S$$ is stress and $$Y$$ is Young's modulus of material of wire, then energy stored in the wire per unit volume is:
  • $$\displaystyle 2{ S }^{ 2 }Y$$
  • $$\displaystyle \frac { S }{ Yx } $$
  • $$\displaystyle \frac { 2Y }{ { S }^{ 2 } } $$
  • $$\displaystyle \frac { { S }^{ 2 } }{ 2Y } $$
Longitudinal strain is possible in 
  • Liquid
  • Gases
  • Solid
  • All of these
The adjacent graph shows the extension ($$\displaystyle \Delta l$$) of a wire of length 1 m suspended from the top of a . roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is $$\displaystyle { 10 }^{ -6 }{ m }^{ 2 }$$, calculate the Young's modulus of the material of the wire.
430637_2822dcb4796d460fad1d6d9a6ec5e4fa.png
  • $$\displaystyle 2\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } }$$
  • $$\displaystyle 2\times { 10 }^{ -11 }{ N }/{ { m }^{ 2 } }$$
  • $$\displaystyle 3\times { 10 }^{ -12 }{ N }/{ { m }^{ 2 } }$$
  • $$\displaystyle 2\times { 10 }^{ -13 }{ N }/{ { m }^{ 2 } }$$
For a given material, the Young's modulus is $$2.4$$ times that of rigidity modulus. Its poisson's ratio is.
  • $$2.4$$
  • $$1.2$$
  • $$0.4$$
  • $$0.2$$
The length of an elastic string is $$a$$ metre when the longitudinal tension is $$4$$N and $$b$$ metre when the longitudinal tension is $$5$$N. The length of the string in metre when longitudinal tension is $$ 9 $$N is :
  • $$a-b$$
  • $$5b-4a$$
  • $$2b-\displaystyle\frac{1}{4}a$$
  • $$4a-3b$$
For a constant hydraulic stress on an object, the fractional change in the object's volume ($$\displaystyle \Delta { V }/{ V }$$) and its bulk modulus (B) are related as: 
  • $$\displaystyle \frac { \Delta V }{ V } \propto B$$
  • $$\displaystyle \frac { \Delta V }{ V } \propto \frac { 1 }{ B } $$
  • $$\displaystyle \frac { \Delta V }{ V } \propto { B }^{ 2 }$$
  • $$\displaystyle \frac { \Delta V }{ V } \propto { B }^{ -2 }$$
The length of a metal wire is $$L_1$$ when the tension is $$T_1$$ and $$L_2$$ when the tension is $$T_2$$. The unstretched length of wire is :
  • $$\displaystyle \frac{L_1+L_2}{2}$$
  • $$\displaystyle \sqrt{L_1L_2}$$
  • $$\displaystyle \frac{T_2L_1-T_1L_2}{T_2-T_1}$$
  • $$\displaystyle \frac{T_2L_1+T_1L_2}{T_2+T_1}$$
A metal wire of length l, area of cross-section A and Young's modulus Y behaves as a spring of spring constant k given by.
  • $$k=\displaystyle\frac{YA}{l}$$
  • $$k=\displaystyle\frac{2YA}{l}$$
  • $$k=\displaystyle\frac{YA}{2l}$$
  • $$k=\displaystyle\frac{Yl}{A}$$
In Young's double slit experiment, the ratio of intensities of bright and dark bands is $$16$$ which means
  • The ratio of their amplitudes is $$5$$
  • Intensities of individual sources are $$25$$ and $$9$$ units respectively
  • The ratio of their amplitudes is $$4$$
  • Intensities of individuals sources are $$4$$ and $$3$$ units respectively
The increase in pressure required in $$kPa$$, to decrease the $$200$$ litres volume of a liquid by $$0.004$$% is (bulk modulus of the liquid $$= 2100\ MPa$$)
  • $$8.4$$
  • $$84$$
  • $$92.4$$
  • $$168$$
Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows
  • L = 100 cm, r = 1 mm
  • L = 200 cm, r = 3 mm
  • L = 300 cm, r = 3 mm
  • L = 400 cm, r = 4 mm
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 $$U$$)
  • $${U}/{5}$$
  • $${U}/{25}$$
  • $$5 U$$
  • $$25 U$$
Two wires A and B are of the same materials. Their lengths are in the ratio $$1:2$$ and the diameters are in the ratio $$2:1$$, When stretched by force $$F_A$$ and $$F_B$$ respectively they get equal increase in their lengths. Then the ratio $$\dfrac{F_A}{F_B}$$ should be:
  • $$1:2$$
  • $$1:1$$
  • $$2:1$$
  • $$8:1$$
There is no change in volume of a wire due to change in its length of stretching. The Poisson's ratio of the material of the wire is:
  • 0.50
  • - 0.50
  • 0.25
  • - 0.25
The value of Poisson's ratio (theoretically) lies between
  • $$-1$$ to $$\dfrac { 1 }{ 2 } $$
  • $$-\dfrac { 3 }{ 4 } $$ to $$-\dfrac { 1 }{ 2 } $$
  • $$-\dfrac { 1 }{ 2 } $$ to $$1$$
  • $$1$$ to $$2$$
Bulk modulus of water is $$2\times 10^9N/m^2$$. The change in pressure required to increase the density of water by $$0.1\%$$ is.
  • $$2\times 10^9N/m^2$$
  • $$2\times 10^8N/m^2$$
  • $$2\times 10^6N/m^2$$
  • $$2\times 10^4N/m^2$$
A tension of $$22$$ N is applied to a copper wire of cross-sectional area $$0.02\ cm^2$$. Young's modulus of copper is $$1.1\times 10^{11}N/m^2$$ and Poisson's ratio $$0.32$$. The decrease in cross sectional area will be:
  • $$1.28\times 10^{-6}cm^2$$
  • $$1.6\times 10^{-6}cm^2$$
  • $$2.56\times 10^{-6}cm^2$$
  • $$0.64\times 10^{-6}cm^2$$
The materials, which do not show a fixed trend of deformation vs. applied force, are called:
  • inelastic materials
  • plastic materials
  • elastic materials
  • rigid materials
A spring is stretched by applying a load to its free end. The strain produced in the spring is
  • Volumetric
  • Shear
  • Longitudinal and shear
  • Longitudinal
The average depth of Indian ocean is about $$3000\ m$$. The value of fractional compression $$ \dfrac{\Delta V}{V}$$ of water at the bottom of the ocean is:
[Given that the bulk modulus of water is $$2.2\times 10^9\ Nm^{-2}$$, $$ g=9.8\ ms^{-2}$$ and $$\rho_{H_2O}=1000\ kg.m^{-3}$$]
  • $$3.4\times 10^{-2}$$
  • $$1.34\times 10^{-2}$$
  • $$4.13\times 10^{-2}$$
  • $$13.4\times 10^{-2}$$
Let L be the length and d be the diameter of cross-section of a wire. Wires of the same material with different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
  • $$L = 200\ cm, d = 0.5\ mm$$
  • $$L = 300\ cm, d = 1.0\ mm$$
  • $$L = 50\ cm, d = 0.05\ mm$$
  • $$L = 100\ cm, d = 0.2\ mm$$
The Poisson's ratio of a material is $$0.5$$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is :
  • 1%
  • 2%
  • 2.5%
  • 4%
A metal rod is fixed rigidly at two ends . If $$L, \alpha$$ and $$Y$$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by $$\triangle T$$, the longitudinal stress developed in the rod is
  • Inversely proportional to $$\alpha$$
  • Inversely proportional to $$Y$$
  • Directly proportional to $$\dfrac{\triangle T}{Y}$$
  • Independent of $$L$$
In the Searle's method to determine the Young's modulus of a wire, a steel wire of length $$156cm$$ and diameter $$0.054\ cm$$ is taken as experimental wire. the average increase in length for $$1.5\ kgwt$$ is found to be $$0.050cm$$. then the Ypung's modulus of the wire is 
  • $$3.002\times 10^{11}N/m^{2}$$
  • $$1.002\times 10^{11}N/m^{2}$$
  • $$2.002\times 10^{11}N/m^{2}$$
  • $$2.5\times 10^{11}N/m^{2}$$
The adjacent graph shows the extension (l) of a wire of length 1 m suspended from the top of a roof at one end and with load 'W' connected to the other end. If the cross-sectional area of the wire is $$ 10^{-6}$$$$m^{-2}$$, calculate the Young modulus of the material of the wire:
596367.jpg
  • $$2 \times 10^{-11}$$
  • $$2 \times 10^{10}$$
  • $$2 \times 10^{11}$$
  • $$ 2 \times 10^{-10}$$

An iron rod of length 2m and cross- sectional area of $$50mm^{2}$$ stretched by 0.5mm, when a mass of 250 kg is hung from its lower end. Young's modulus of iron rod is 
  • $$\displaystyle19.6\times 10^{20} N/m^{2}$$
  • $$\displaystyle19.6\times 10^{18} N/m^{2}$$
  • $$\displaystyle19.6\times 10^{10} N/m^{2}$$
  • $$\displaystyle19.6\times 10^{15} N/m^{2}$$
A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?
  • Youngs modulus
  • Shear modulus
  • Poissons ratio
  • both Youngs modulus and Shear modulus
0:0:1


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