CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 7 - MCQExams.com

A wire of initial length $$L$$ and radius $$r$$ is stretched by a length $$l$$. Another wire of same material but with initial length $$2L$$ and radius $$2r$$ is stretched by a length $$2l$$. The ratio of the stored elastic energy per unit volume in the first and second wire is,
  • 1 : 4
  • 1 : 2
  • 2 : 1
  • 1 : 1
A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm are connected end to end. When stretched by a force, the elonation in length 0.50 mm is produced in the copper wire. The stretching force is
$$(Y_{cu}=1.1\times 10^{11}N/m^2, Y_{steel}=2.0\times 10^{11}N/m^2)$$
  • $$5.4\times 10^2N$$
  • $$3.6\times 10^2N$$
  • $$2.4\times 10^2N$$
  • $$1.8\times 10^2N$$
A and B are two steel wires and the radius of A is twice that of B, if they are stretched by the same load, then the stress on B is ...........
  • Four times that of A.
  • Two times that of A.
  • Three times that of A.
  • Same as that A.
A wire of length L and of cross-sectional area A is made of a material of Young's modulus Y. The work done in stretching the wire by an amount $$x$$ is given by :
  • $$\dfrac{YAx^2}{L}$$
  • $$\dfrac{YAx^2}{2L}$$
  • $$\dfrac{YAL^2}{x}$$
  • $$\dfrac{YAL^2}{2x}$$
If longitudinal strain for a wire is $$0.03$$ and its poisson ratio is $$0.5$$, then its lateral strain is
  • $$0.003$$
  • $$0.0075$$
  • $$0.015$$
  • $$0.4$$
When the tension in a metal wire is $$ T_1$$ its length is $$ l_1 , $$ when the tension is $$ T_2$$ its length is $$ l_$$ The natural length of wire is :
  • $$ T_1l_1 + T_2 l_2 $$
  • $$ \dfrac {l_1 T_2 - l_2 T_1}{T_2 - T_1}$$
  • $$ \dfrac {l_1 T_2 - l_2 T_1}{T_2 + T_1}$$
  • $$ \dfrac {T_2} {T_1} ( l_1 + l_2 ) $$
Stretching of a rubber band results in ___________.
  • No change in potential energy
  • Zero value of potential energy
  • Increase in potential energy
  • Decrease in potential energy
A liquid of bulk modulus $$k$$ is compressed by applying an external pressure such that its density increases by $$0.01$$%. The pressure applied on the liquid is:
  • $$\cfrac { k }{ 10000 } $$
  • $$\cfrac { k }{ 1000 } $$
  • $$1000k$$
  • $$0.01k$$
One end of a slack wire (Youngs modulus $$Y$$, length $$L$$ and cross -sectional area A) is clamped to a rigid wall and the other end to a block (mass m) which rests on a smooth horizontal plane. The block is set in motion with a speed v. What is the maximum distance the block will travel after the wire becomes taut?
  • $$v\sqrt {\dfrac {mL}{AY}}$$
  • $$v\sqrt {\dfrac {2mL}{AY}}$$
  • $$v\sqrt {\dfrac {mL}{2AY}}$$
  • $$L\sqrt {\dfrac {mv}{AY}}$$
The relation between Young's modulus $$Y$$, bulk modulus $$K$$ and modulus of elasticity $$\sigma$$ is
  • $$\cfrac { 1 }{ y } =\cfrac { 1 }{ k } +\cfrac { 3 }{ \eta } $$
  • $$\cfrac { 3 }{ y } =\cfrac { 1 }{ \eta } +\cfrac { 1 }{ 3k } $$
  • $$\cfrac { 1 }{ y } =\cfrac { 3 }{ \eta } +\cfrac { 1 }{ 3k } $$
  • $$\cfrac { 1 }{ \eta } =\cfrac { 3 }{ y } +\cfrac { 1 }{ 3k } $$
The area of cross-section of a steel wire $$\left( Y=2.0\times { 10 }^{ 11 }{ N }/{ { m }^{ 2 } } \right)$$ is $$0.1 { cm }^{ 2 }$$. The force required to double its length will be :
  • $$2\times { 10 }^{ 12 }N$$
  • $$2\times { 10 }^{ 11 }N$$
  • $$2\times { 10 }^{ 10 }N$$
  • $$2\times { 10 }^{ 6 }N$$
Two wires of same material and same diameter have lengths in the ratio 2 :They are stretched by the same force. The ratio of work done in stretching them is :
  • 5 : 2
  • 2 : 5
  • 1 : 3
  • 3 : 1
A metallic rod of length $$l$$ and cross sectional area $$A$$ is made of a material of Young's modulus $$Y$$. If the rod is elongated by an amount $$y$$, then the work done is proportional to
  • $$y$$
  • $$1/y$$
  • $${ y }^{ 2 }$$
  • $$1/{ y }^{ 2 }$$
Young's modulus of rubber is $$10^4$$ N$$/m^2$$ and area of cross-section is $$2$$ $$cm^2$$. If force of $$2\times 10^5$$ dyne is applied along its length, then its final length becomes.
  • $$3L$$
  • $$4L$$
  • $$2L$$
  • None of these
A rubber cord catapult has cross-sectional area 25 mm$$^2$$ and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 g. Taking $$Y_{rubber} = 5 \times 10^8 Nm^{-2}$$, velocity of projected missile is:
  • 20 ms$$^{-1}$$
  • 100 ms^{-1}$$
  • 250 ms$$^{-1}$$
  • 200 ms$$^{-1}$$
The bulk modulus of an ideal gas at constant temperature is :
  • Equal to its pressure
  • Equal to its volume
  • Equal to $${ p }/{ 2 }$$
  • Cannot be determined
A ball falling-in a lake of depth 400 m has a decrease of $$0.2\%$$ in its volume at the bottom. The bulk modulus of the material of the ball is (in $$Nm^-{2}$$)
  • $$9.8 \times 10^9$$
  • $$9.8 \times 10^{10}$$
  • $$1.96 \times 10^{10}$$
  • $$9.8 \times 10^{11}$$
  • $$1.96 \times 10^9$$
One end of a uniform bar of weight $$\displaystyle { w }_{ 1 }$$ is suspended from the roof and a weight $$\displaystyle { w }_{ 2 }$$ is suspended from the other end, the area of cross-section is A. What is the stress at the mid point of the rod?
  • $$\displaystyle \frac { { w }_{ 1 }+{ w }_{ 2 } }{ A } $$
  • $$\displaystyle \frac { { w }_{ 1 }-{ w }_{ 2 } }{ A } $$
  • $$\displaystyle \frac { \left( { { w }_{ 1 } }/{ 2 } \right) +{ w }_{ 2 } }{ A } $$
  • $$\displaystyle \frac { { { w }_{ 2 } }/{ 2 }+{ w }_{ 1 } }{ A } $$
The Poisson's ratio of a material is $$0.8$$. If a force is applied to a wire of this material decreases its cross-sectional area by $$4\%$$, then the percentage increase in its length will be.
  • $$1\%$$
  • $$2\%$$
  • $$2.5\%$$
  • $$4\%$$
An aluminium rod (Young's modulus $$= 7\times 10^{9} N/m^{2})$$ has a breaking strain of $$0.2$$%. The minimum cross-sectional area of the rod in order to support a load of $$10^{4}$$ Newton's is:
  • $$1\times 10^{-2}m^{2}$$
  • $$1.4\times 10^{-3}m^{2}$$
  • $$3.5\times 10^{-3}m^{2}$$
  • $$7.1\times 10^{-4}m^{2}$$
The compressibility of water $$4\times 10^{-5}$$ per unit atmospheric pressure. The decrease in volume of $$100\ cubic$$ centimeter of water under a pressure of $$100$$ atmosphere will be:
  • $$0.4\ cc$$
  • $$4\times 10^{-5} cc$$
  • $$0.025\ cc$$
  • $$0.004\ cc$$
One end of a long metallic wire of length $$L$$ is tied to the ceiling. The other end is tied to massless spring of spring constant $$k$$. A mass $$m$$ hangs freely from the free end of the spring. The area of cross-section and Young's modulus of the wire are $$A$$ and $$Y$$ respectively. If the mass is slightly pulled down and released, it will oscillate with a time period $$T$$ equal to
  • $$2\pi \sqrt {m/k}$$
  • $$2\pi \sqrt {\dfrac {m(YA + kL)}{YAk}}$$
  • $$2\pi \sqrt {\dfrac {mYA}{kL}}$$
  • $$2\pi \sqrt {\dfrac {mL}{YA}}$$
The load versus elongation graph for four wires of the same material and same length is shown in the figure. The thinnest wire is represented by the line.
789435_851b4396bf6741d29a5b390507c74e4f.png
  • $$OA$$
  • $$OB$$
  • $$OC$$
  • $$OD$$
A cubical ball is taken to a depth of $$200 m$$ in a sea. The decrease in volume observed to be $$0.1$$%. The bulk modulus of the ball is - $$(g = 10/ m/s^{-2})$$
  • $$2\times 10^{7} Pa$$
  • $$2\times 10^{6} Pa$$
  • $$2\times 10^{9} Pa$$
  • $$1.2\times 10^{9} Pa$$
A uniform rod of length $$'L'$$ and density $$'\rho'$$ is being pulled along a smooth floor with horizontal acceleration $$\alpha$$ as shown in the figure. The magnitude of the stress at the transverse cross-section through the mid-point of the rod is _________.
713914_6f81dd00820142b3a084210a500e84b7.png
  • $$\dfrac {\rho l \alpha}{4}$$
  • $$4\rho l\alpha$$
  • $$2\rho l\alpha$$
  • $$\dfrac {\rho l\alpha}{2}$$
Which of the following statements are correct?
  • Poisson's ratio can be greater than $$0.5$$
  • Poisson's ratio is a characteristic property of the material of the body
  • Poisson's ratio of a body depends upon its shape and size
  • None of these
The bulk modulus of water is $$2.0\times { 10 }^{ 9 }\ { N }/{ { m }^{ 2 } }$$ . The pressure required to increase the density of water $$0.1 \%$$ is
  • $$2.0\times { 10 }^{ 3 }\ { N }/{ { m }^{ 2 } }$$
  • $$2.0\times { 10 }^{ 6 }\ { N }/{ { m }^{ 2 } }$$
  • $$2.0\times { 10 }^{ 5 }\ { N }/{ { m }^{ 2 } }$$
  • $$2.0\times { 10 }^{ 7 }\ { N }/{ { m }^{ 2 } }$$
Figure shows the strain-stress curve for a given material. The Young's modulus of the material is 
936727_3b7ead2d5dc3489285ffad173ef41824.PNG
  • $$5\times { 10 }^{ 9 }N\quad { m }^{ -2 }$$
  • $$5\times { 10 }^{ 10 }N\quad { m }^{ -2 }$$
  • $$7.5\times { 10 }^{ 9 }N\quad { m }^{ -2 }$$
  • $$7.5\times { 10 }^{ 10 }N\quad { m }^{ -2 }$$
A uniform slender rod of length $$L$$, cross-sectional area $$A$$ and Young's modulus $$Y$$ is acted upon by the forces shown in the figure. The elongation of the rod is:
876281_0cf30a6f10c247adb47a8ceecb09ebb0.png
  • $$\displaystyle \dfrac{3FL}{5AY}$$
  • $$\displaystyle \dfrac{2FL}{5AY}$$
  • $$\displaystyle \dfrac{3FL}{8AY}$$
  • $$\displaystyle \dfrac{8FL}{3AY}$$
Identical springs of steel and copper $$\left( { Y }_{ steel }>\quad { Y }_{ copper } \right) $$ are equally stretched
  • Less work is done on copper spring
  • Less work is done on steel spring
  • Equal work is done on both the springs
  • Data is incomplete
Stress is a ______ quantity.
  • scalar
  • vector
  • tensor
  • dimensionless
Two wires of equal length and cross-sectional area are suspended as shown in figure. Their Young's modulii are Y$$_1$$ and Y$$_2$$ respectively. The equivalent Young's modulii will be:
874226_2b3ddaab5a6d4119873df2b1840b2835.png
  • $$\displaystyle Y_1 + Y_2$$
  • $$\displaystyle \frac{Y_1 Y_2}{Y_1 + Y_2}$$
  • $$\displaystyle \frac{Y_1 + Y_2}{2}$$
  • $$\displaystyle \sqrt{Y_1 Y_2}$$
To determine the Young's modulus of a wire, the formula is $$Y = \dfrac {F}{A}, \dfrac {L}{\triangle l}$$; where $$L = length, A =$$ area of cross-section of the wire, $$\triangle L =$$ Change in length of the wire when stretched with a force $$F$$. The conversion factor to change it from $$CGS$$ to $$MKS$$ system is
  • $$1$$
  • $$10$$
  • $$0.1$$
  • $$0.01$$
Match the Column I with Column II
Column IColumn II
(A) A body which regains its original shape after the removal
of external forces		(p) Elasticity
(B) A body which does not regain its original shape after the removal
of external forces.		(q) Elastic body
(C) A body which does not show any deformation on applying external
forces		(r) Plastic
body
(D) The property of the body to regain its original configuration when
the deforming forces are removed.		(s) Rigid
 body
  • A-q, B-r, C-s, D-p
  • A-p, B-q, C-r, D-s
  • A-r, B-s, C-p, D-q
  • A-s, B-p, C-q, D-r.
Which of the following statements is correct regarding Poisson's ratio?
  • It is the ratio of the longitudinal strain to the lateral strain
  • Its value is independent of the nature of the material
  • It is unitless and dimensionless quantity
  • The practical value of Poisson's ratio lies between $$0$$ and $$1$$
The area of cross section of a steel wire ($$y=2\times { 10 }^{ 11 }N/{ m }^{ 2 }$$) is $$0.1{cm}^{2}$$. The force required to double its length will be:
  • $$2\times { 10 }^{ 12 }N$$
  • $$2\times { 10 }^{ 11 }N$$
  • $$2\times { 10 }^{ 10 }N$$
  • $$2\times { 10 }^{ 6 }N$$
Identical springs of steel and copper $$\left( { Y }_{ steel }>{ Y }_{ copper } \right) $$ are equally stretched then:
  • Less work is done on copper spring
  • Less work is done on steel spring
  • Equal work is done on both the springs
  • Data is incomplete
A wire stretches by a certain amount under a load. If the load and radius both are increased to four times. The stretch caused in the wire is then
  • $$l$$
  • $$\cfrac { l }{ 2 } $$
  • $$\cfrac { l }{ 3 } $$
  • $$\cfrac { l }{ 4 } $$
When the load on a wire is increased from $$3kg$$ $$wt$$ to $$5kg$$ $$wt$$ the elongation increases from $$0.61mm$$ to $$1.02mm$$. The required work done during the extension of the wire is:
  • $$16\times { 10 }^{ -3 }J$$
  • $$8\times { 10 }^{ -2 }J$$
  • $$20\times { 10 }^{ -2 }J\quad $$
  • $$11\times { 10 }^{ -3 }J$$
Let $${Y}_{S}$$ and $${Y}_{A}$$ represent Young's modulus for steel and aluminium respectively It is said that steel is more elastic than aluminium. Therefore, it follows that
  • $${ Y }_{ S }={ Y }_{ A }$$
  • $${ Y }_{ S }< { Y }_{ A }$$
  • $${ Y }_{ S }> { Y }_{ A }$$
  • $$\cfrac { { Y }_{ S } }{ { Y }_{ A } } =0$$
A $$15kg$$ mass fastened to the end of a steel wire of unstretched length $$1.0m$$ is whirled in a vertical circle with an angular velocity of $$2rev$$ $${s}^{-1}$$ at the bottom of the circle. The cross-section of the wire is $$0.05{cm}^{2}$$. The elongation of the wire when the mass is at the lowest point of its path is
(Take $$g=10m{ s }^{ -2 },{ Y }_{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 }\quad $$)
  • $$0.52mm$$
  • $$1.52mm$$
  • $$2.52mm$$
  • $$3.52mm$$
A steel rod of length $$1m$$ and radius $$10mm$$ is stretched by a force $$100kN$$ along its length. The percentage strain in the rod is then
 $$\left( { Y }_{ steel }=2\times { 10 }^{ 11 }N\quad { m }^{ -2 } \right) $$
  • $$0.04$$%
  • $$0.08$$%
  • $$0.16$$%
  • $$0.24$$%
If the work done in stretching a wire by $$1mm$$ is $$2J$$, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by $$1mm$$ is:
  • $$16J$$
  • $$8J$$
  • $$4J$$
  • $$\cfrac { 1 }{ 4 } J$$
A wire of length $$L$$ has a linear mass density $$\mu$$ and area of cross-section $$A$$ and Young's modulus $$Y$$ is suspended vertically from a rigid support. The extension produced in the wire due to its own weight is:
  • $$\cfrac { \mu g{ L }^{ 2 } }{ YA } $$
  • $$\cfrac { \mu g{ L }^{ 2 } }{ 2YA } $$
  • $$\cfrac { 2\mu g{ L }^{ 2 } }{ YA } $$
  • $$\cfrac { 2\mu g{ L }^{ 2 } }{ 3YA } $$
The following four wires of length $$L$$ and radius $$r$$ are made of the same material. Which of these will have the largest extension, when the same tension is applied?
  • $$L=100cm, r=0.2mm$$
  • $$L=200cm, r=0.4mm$$
  • $$L=300cm, r=0.6mm$$
  • $$L=400cm, r=0.8mm$$
Two wires of the same material and length but diameter in the ratio $$1:2$$ are stretched by the same load. The ratio of elastic potential energy per unit volume for the two wires is:
  • $$1:1$$
  • $$2:1$$
  • $$4:1$$
  • $$16:1$$
Among solids, liquids and gases, which posses the greatest bulk modulus?
  • Solids
  • Liquids
  • Gases
  • Both solids and liquids
The average depth of Indian Ocean is about $$3000m$$. The fractional compression, $$\cfrac { \Delta V }{ V } $$ of water at the bottom of the ocean is then
(Given: Bulk modulus of the water$$=2.2\times { 10 }^{ 9 }N{ m }^{ -2 }$$ and $$g=10m{ s }^{ -2 }$$)
  • $$0.82$$%
  • $$0.91$$%
  • $$1.36$$%
  • $$1.24$$%
Match the column I with column II
Column IColumn II
(A) The of shape rubber heel
changes under stress		(p) Young's modulus of elasticity is involved
(B) In a suspended bridge, there is a strain in the ropes by the load of the bridge(B) Bulk modulus of elasticity is involved
(C) In an automobile tyre, when air is compressed, the shape of tyre changes(r) Modulus of rigidity is involved
(D) A solid body is subjected to a deforming force(s) All the moduli of elasticity are involved
  • A-q; B-r; C-s; D-p
  • A-p; B-q; C-r; D-s
  • A-r; B-q; C-p; D-s
  • A-r; B-p; C-q; D-s
The length of a rubber cord is $${l}_{1}$$ when the tension is $$4N$$ and $${l}_{2}m$$ when the tension is $$6N$$. The length when the tension is $$9N$$, is:
  • $$\left( 2.5{ l }_{ 2 }-1.5{ l }_{ 1 } \right) m$$
  • $$\left( 6{ l }_{ 2 }-1.5{ l }_{ 1 } \right) m$$
  • $$\left( 3{ l }_{ 2 }-2{ l }_{ 1 } \right) m$$
  • $$\left( 3.5{ l }_{ 2 }-2.5{ l }_{ 1 } \right) m$$
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