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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 1mm2, then the Young's modulus of the material  of the wire .( In graph, X-axis 1 unit =  10mm)  .
289752.png
  • 2×1011Nm1
  • 2×1010Nm2
  • 12×1011Nm2
  • None of these
Copper wire of length 3m and area of cross-section 1mm2, passes through an arrangement of two frictionless pulleys, P1 and P2. One end of the wire is rigidly clamped and a mass of 1kg is hanged from the other end. If Young's modulus for copper is 10×1010N/m2, the elongation in the wire is :

282783_2a7f78b5a04546608c330f0aa26465ba.png
  • 0.05mm
  • 0.1mm
  • 0.2mm
  • 0.3mm
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 =2100MPa):
  • 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:-
  • 19.6×108N/m2
  • 19.6×1010N/m2
  • 19.6×1010N/m2
  • 19.6×108N/m2
A steel wire 1.5m long and of radius 1mm is attached with a load 3kg 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=2×1011N/m2 and g=10m/s2)

  • 1.77×103m
  • 7.17×103m
  • 3.17×107m
  • 1.37×107m
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=1×1011N/m2 with length 6m and a steel wire having Y=2×1011N/m2 with  length 4m each of cross section 105m2 are fastened end to end stretched by a tension of 100N. The elongation produced in the copper wire is :
  • 0.2mm
  • 0.4mm
  • 0.6mm
  • 0.8mm
The bulk modulus of rubber is 9.8×108N/m2. To what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1% ?
  • 1km
  • 25km
  • 100km
  • 200km
When a force is applied on a wire of uniform cross-sectional area 3×106m2 and length 4m, the increase in length is 1 mm. Energy stored in it will be (Y=2×1011N/m2):
  • 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 1×103kg/m3andg=10m/s2 then the volume elasticity in N/m2 will be
  • 108
  • 2×108
  • 109
  • 2×109
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 4N and b metre when the longitudinal tension is 5N. 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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