CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 8 - MCQExams.com

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by $$0.1$$%
(Take density of sea water $${ 10 }^{ 3 }kg\quad { m }^{ -3 }$$, bulk modulus of rubber $$=9\times { 10 }^{ 8 }N{ m }^{ -2 },g=10m{ s }^{ -2 }$$)
  • $$9m$$
  • $$18m$$
  • $$90m$$
  • $$180m$$
A copper wire of length $$2.4m$$ and a steel wire of length $$1.6m$$, both the diameter $$3mm$$, are connected end to end. When stretched by a load, the net elongation is found to be $$0.7mm$$. The load applied is
$$\left( { Y }_{ copper }=1.2\times { 10 }^{ 11 }N\quad { m }^{ -2 },{ Y }_{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 } \right) $$
  • $$1.2\times { 10 }^{ 2 }N$$
  • $$1.8\times { 10 }^{ 2 }N$$
  • $$2.4\times { 10 }^{ 2 }N$$
  • $$3.2\times { 10 }^{ 2 }N$$
The volume change of a solid copper cube $$10cm$$ on an edge, when subjected to a pressure of $$7MPa$$ is then
(Bulk modulus of copper $$=140GPa$$)
  • $$5\times { 10 }^{ -2 }{ cm }^{ 3 }$$.
  • $$10\times { 10 }^{ -2 }{ cm }^{ 3 }$$
  • $$15\times { 10 }^{ -2 }{ cm }^{ 3 }$$
  • $$20\times { 10 }^{ -2 }{ cm }^{ 3 }$$
Which of the following apparatus is used to determine the Young's modulus of the material of a given wire?
  • Searle
  • sonometer
  • Metre bridge
  • Resonance tube
A copper wire of length $$2.4m$$ and a steel wire of length $$1.6m$$, both the diameter $$3mm$$, are connected end to end. The ratio fo elongation of steel to the copper wires is then
$$\left( { Y }_{ copper }=1.2\times { 10 }^{ 11 }N\quad { m }^{ -2 },{ Y }_{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 } \right) $$
  • $$\cfrac { 5 }{ 2 } $$
  • $$\cfrac { 2 }{ 5 } $$
  • $$\cfrac { 3 }{ 2 } $$
  • $$\cfrac { 2 }{ 3 } $$
The relation between $$Y, \eta$$ and $$B$$ where $$Y, \eta ,B$$ are Young's Modulus, Shear modulus and bulk modulus respectively.
  • $$\cfrac { 1 }{ Y } =\cfrac { 1 }{ 3\eta } +\cfrac { 1 }{ 9B } $$
  • $$\cfrac { 9 }{ Y } =\cfrac { 1 }{ 3\eta } +\cfrac { 3 }{ B } $$
  • $$\cfrac { 1 }{ \eta } =\cfrac { 1 }{ B } +\cfrac { 1 }{ Y } $$
  • $$\cfrac { 9 }{ Y } =\cfrac { 3 }{ \eta } +\cfrac { 1 }{ B } $$
If in the above question, the Young's modulus of the material is Y, the value of extension x is:
  • $$\left ( \frac{El}{YA} \right )^{1/3}$$
  • $$\left ( \frac{YA}{Wl} \right )^{1/3}$$
  • $$\frac{1}{l}\left [ \frac{WA}{Y} \right ]^{1/3}$$
  • $$l\left [ \frac{W}{YA} \right ]^{1/3}$$
A metal wire of length $$L_1$$ and area of cross section A is attached to a rigid support. Another metal wire of length $$L_2$$ and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If $$Y_1$$ and $$Y_2$$ are the Young's moduli of the wires respectively, the effective force constant of the system of two wires is
  • $$\frac{Y_1Y_2A}{2(Y_1L_2+Y_2L_1)}$$
  • $$\frac{Y_1Y_2A}{2(L_1L_2)^{1/2}}$$
  • $$\frac{Y_1Y_2A}{(Y_1L_2+Y_2L_1)}$$
  • $$\frac{(Y_1Y_2)^{1/2}A}{2(L_1L_2)^{1/2}}$$
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
  • remains same
A steel bar $$ABCD$$ $$40cm$$ long is made up of three parts $$AB, BC$$ and $$CD$$, as shown in the figure The rod is subjected to a pull of $$25kN$$. The total extension of the rod is (Young's modulus for steel $$2\times { 10 }^{ 11 }N{ m }^{ -2 }$$:
937129_3313c973251549d08a44bfd84cbcd489.png
  • $$0.0637mm$$
  • $$0.0647mm$$
  • $$0.0657mm$$
  • $$0.0667mm$$
The mean distance between the atoms of iron is $$3\times10^{-10}m$$ and interatomic force constant for iron is $$7 N m^{-1}$$. The Young's modulus of electricity for iron is 
  • $$2.33\times 10^5 Nm^{-2}$$
  • $$23.3\times 10^{10} Nm^{-2}$$
  • $$2.33\times 10^{9} Nm^{-2}$$
  • $$2.33\times 10^{10} Nm^{-2}$$
Find the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $$ 57^o C $$ is drunk. (Take temperature of tooth to be $$ 37^o C,\alpha =1.7\times { 10 }^{ -5 }{ }{ /^o C} $$ and bulk modulus for copper $$ =140\times { 10 }^{ 9 }N{ m }^{ -2 } $$ ) 
  • $$ 1.43\times { 10 }^{ 8 }N{ m }^{ -2 } $$
  • $$ 4.13\times { 10 }^{ 8 }N{ m }^{ -2 } $$
  • $$ 2.12\times { 10 }^{ 4 }N{ m }^{ -2 } $$
  • $$ 3.12\times { 10 }^{ 4 }N{ m }^{ -2 } $$
The adjacent graph shows the extension ($$\Delta l$$) of a wire of length $$1m$$ 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 $${ 10 }^{ -6 }{ m }^{ 2 }$$, the Young's modulus of the material of the wire is
937214_48e2987e0eec45bf9a5bdc9eb1ead15a.png
  • $$2\times { 10 }^{ 11 }N{ m }^{ 2 }$$
  • $$2\times { 10 }^{ -11 }N{ m }^{ 2 }$$
  • $$3\times { 10 }^{ -12 }N{ m }^{ 2 }$$
  • $$2\times { 10 }^{ -13 }N{ m }^{ 2 }$$
The ratio of diameters of two wires of same material is n:The length of  each wire is 4 m. On applying the same load, the increases in the length of the thin wire will be (n > l) 
  • $$n^2$$ times
  • n times
  • 2n times
  • (2n + 1) times
The dimensions of four wires of the same material are given below. In which wire the increase in the length will be maximum?
  • Length 100 cm, diameter 1 mm
  • Length 200 cm, diameter 2 mm
  • Length 300 cm. diameter 3 mm
  • Length 50 cm, diameter 0.5 mm
A rubber ball of bulk modulus B is taken to a depth h of a liquid of density p. Find the fractional change in the radius of the ball. 

  • $$ \, \dfrac{\rho gh}{4B}$$

  • $$ \, \dfrac{\rho gh}{3B}$$

  • $$\, \dfrac{\rho gh}{2B}$$

  • $$ \dfrac{\rho gh}{5B}$$
A wire is stretched 1 mm by a force of 1 kN. How far would a wire of the same  material and length but of four times that diameter he stretched by the same  force?
  • $$\dfrac{1}{2}$$mm
  • $$\dfrac{1}{4}$$mm
  • $$\dfrac{1}{8}$$mm
  • $$\dfrac{1}{16}$$mm
A steel wire is stretched by 1 kg wt. If the radius of the wire is doubled,  its Young's modulus will:
  • remain unchanged
  • become half
  • become double
  • become four times
 Plastic deformation results from the following 
  • Slip
  • Twinning
  • Both slip and twinning
  • creep
A gas undergoes a process in which its pressure $$p$$ and value $$v$$ are related as $$Vp^2 =$$ constant. The bulk modulus for the gas in this process is:
  • $$\dfrac{p}{2}$$
  • $$2p$$
  • $$2pv$$
  • $$3p$$
A wire has a tensile strength of 70MPa, and breaks under 100N of force. What is the cross-sectional area of the wire just before breaking?
  • $$14.2 \times 10^{-6} m^2$$
  • $$1.42 \times 10^{-6} m^2$$
  • $$ 1.42 \times 10^{-3} m^2$$
  • $$ 1.42 \times 10^{-2} m^2$$
A thin metal sheet is being bent by or pounded in to a new shape. The process of being elastic to plastic behaviour is known as 
  • Yield
  • Creep
  • Welding
  • Tinkering
An elastic spring is given a force of 1000 N over an area of $$0.2 m^2.$$
  • $$3000 N m^{-2}$$
  • $$5000 N m^{-2}$$
  • $$500 N m^{-2}$$
  • $$2500 N m^{-2}$$
The plasticity behaviour of a material determines the 
  • elastic behavior of the material
  • resistance of the material to electric fields
  • viscous behavior of the material and is irrecoverable.
  • resistance of the material to magnetic fields
Substances that elongate considerably and undergo plastic deformation before they break are known as
  • brittle substances
  • breakable substances
  • ductile substances
  • all of these
Plastic deformation in a material begins at
  • Q point
  • Yield point
  • Proportionality limit
  • Elastic limit
At yield point, Hooke's law doesn't hold good
  • True
  • False
Elasticity is defined as the ability of a body to 
  • Resist linear motion in a hard surface
  • Resist rolling motion in a hard surface
  • Resist a distorting influence and to return to its original size and shape when that influence or force is removed.
  • Resist electric current in a magnetic field
Which of the following is the dimension of Bulk Modulus?
  • $$[M^1L^{-1}T^{-1}]$$
  • $$[M^1L^{-1}T^{-2}]$$
  • $$[M^1L^{1}T^{2}]$$
  • $$[M^1L^{1}T^{-1}]$$
Longitudinal strain is calculated using the formula
  • Change in length/ original length
  • Original length/Change in length
  • Original length $$\times $$ Change in length
  • Original length - Change in length
Poisson' ratio is defined as the ratio of 
  • longitudinal stress and longitudinal strain
  • longitudinal stress and lateral stress
  • lateral stress and longitudinal stress
  • lateral stress and lateral strain
The difference between pressure and stress is 
  • pressure and stress have different units
  • pressure and stress have different dimensions
  • Force cannot be determined using stress, but in pressure it can be done
  • Pressured is applied to a body, while stress is induced
Which one of the following is true about Bulk Modulus of elasticity?
  • It is the ratio of compressive stress to volumetric strain
  • It is the ratio of compressive stress to linear strain
  • It is the ratio of tensile stress to volumetric strain
  • It is the ratio of tensile stress to linear strain
A force of 10 N is applied to an object, whose area is $$5 cm^2$$ at an angle of 30 degrees with the vertical. What kind of stress can be found from this data
  • Normal and areal stress can be found
  • only normal stress can be found
  • only areal stress can be found
  • Stress cannot be found from this data, since applied force is neither along the horizontal or vertical
A steel wire is suspended from a fixed end, while the other end is loaded with a weight W. This produced an extension x. As the weight is increased, the extension was also increased. A plot of extension vs load within elastic limits will give rise to 
  • a curve
  • an ellipse
  • a straight line
  • a hyperbola
The radius of a copper wire is 4 mm. What force is required to stretch the wire by 20% of its length, assuming that the elastic limit is not exceeded (Y=$$12 \times 10^{10} N / m^2$$
  • $$7.23 \times 10^5 N$$
  • $$7.23 \times 10^7 N$$
  • $$7.23 \times 10^6 N$$
  • $$7.23 \times 10^8 N$$

A wire of length L can support a load W. If the wire is broken in to two equal parts , then how much load can be suspended by one of those cut wires?
  • Half
  • Same
  • Double
  • One fourth

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight. ( [Density of rubber is $$1500 (kg / m^3), Y = 5 \times 10^8 N/m^2)$$
  • 0.3 mm
  • 0.15 mm
  • 0.015 mm
  • 0.03 mm
When the 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 changes by $$10$$%. The bulk modulus is
  • $$1.55\times10^5 \,Pa$$
  • $$1.05\times10^5 \,Pa$$
  • $$1.4\times10^5 \,Pa$$
  • $$0.115\times10^5 \,Pa$$
A student measures the poisson's ratio to be greater than 1 in an experiment. The meaning of this statement would be
  • An increase in length would also result in decrease in area of cross section of the wire
  • An increase in length would also result in increase in area of cross section of the wire
  • An decrease in length would also result in decrease in area of cross section of the wire
  • An increase in length will not change the area of cross section of the wire
The theoretical limits of poisson's ratio lies between -1 to 0.5 because
  • Shear modulus and bulk's modulus should be positive
  • Bulk's modulus is negative during compression
  • Shear modulus is negative during compression
  • Young's modulus should be always positive
A $$1$$m long metal wire of cross sectional area $$10^{-6}m^2$$ is fixed at one end from a rigid support and a weight W is hanging at its other end. The graph shows the observed extension of length $$\Delta l$$ of the wire as a function of W. Young's modulus of material of the wire in SI units is?
1010213_a399a32c8ad148bd828780acd9113058.png
  • $$5\times 10^4$$
  • $$2\times 10^5$$
  • $$2\times 10^{11}$$
  • $$5\times 10^{11}$$
A uniform wire (Young's modulus $$2\times 10^{11}Nm^{-2}$$ ) is subjected to longitudinal tensile stress of $$5\times 10^7\ Nm^{-2}$$. If the overall volume change in the wire is $$0.02\%$$,  the frictional decrease in the radius of the wire is close to  
  • $$1.0 \times 10^{-4}$$
  • $$1.5 \times 10^{-4}$$
  • $$0.25 \times 10^{-4}$$
  • $$5 \times 10^{-4}$$
The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept inside the container is $$1:4$$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all the temperature?
  • $$2/5$$
  • $$1/4$$
  • $$1/64$$
  • $$1/8$$
A metal rod of Young's modulus $$Y$$ and coefficient of thermal expansion $$\alpha$$ is held at its two ends such that its length remains invariant. If its temperature is raised by $${t}^{o}C$$, the linear stress developed in it is:
  • $$1/\left( Y\alpha t \right) $$
  • $$\alpha t/Y$$
  • $$Y/\alpha t$$
  • $$Y\alpha T$$
For which material the poisson's ratio is greater than 1
  • Steel
  • Copper
  • Aluminium
  • None of the above
The maximum strain energy that can be stored in a body is known as:
  • impact energy
  • toughness
  • proof resilience
  • none of the above
A rubber ball is taken to depth $$1$$ km inside water so that its volume reduces by $$0.05\% $$.What is the bulk modulus of the rubber:
  • $$2 \times 10^{10} N/m^2$$
  • $$2 \times {10^{9\,}}\,N/{m^2}$$
  • $$2 \times 10^{7}N/m^2$$
  • $$2 \times {10^{11\,}}\,N/{m^2}$$
The proportional limit of steel is $$8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$ and its Young's modulus is $$2\times { 10 }^{ 11 }N/{ m }^{ 2 }$$. The maximum elongation, a one metre long steel wire can be given without exceeding the proportional limit is 
  • 2 mm
  • 4 mm
  • 1 mm
  • 8 mm
Overall changes in volume and radii of a uniform cylindrical steel sire are $$0.2\%$$ and $$0.002\%$$ respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is :-
$$(Y=2.0\times 10^{11}\ NM^{-2})$$
  • $$3.2\times 10^{9}\ Nm^{-2}$$
  • $$3.2\times 10^{7}\ Nm^{-2}$$
  • $$3.6\times 10^{9}\ Nm^{-2}$$
  • $$3.9\times 10^{8}\ Nm^{-2}$$
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