CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 1 - MCQExams.com

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area $$A$$ and wire 2 has cross- sectional area $$3A$$. If the length of wire 1 increases by $$\Delta \mathrm{x}$$ on applying force $$\mathrm{F}$$, how much force is needed to stretch wire 2 by the same amount  ?
  • $$\mathrm{F}$$
  • $$4\mathrm{F}$$
  • $$6\mathrm{F}$$
  • $$9\mathrm{F}$$
Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored of their unit volume is $$1:4$$, the ratio of their diameters is:
  • $$2:1$$
  • $$1:\sqrt 2$$
  • $$1:2$$
  • $$\sqrt 2 :1$$
At $$40^oC$$, a brass wire of $$1 mm$$ radius is hung from the ceiling. A small mass, $$M$$ is hung from the free end of the wire. When the wire is cooled down from $$40^oC$$ to $$20^oC$$ it regains its original length of $$0.2 m$$. The value of $$M$$ is close to :
(Coefficient of linear expansion and Young's modulus of brass are $$10^{-5} / ^oC$$ and $$10^{11} \ N/m^2$$, respectively; $$g = 10 ms^{-2}$$)
  • $$1.5\ kg$$
  • $$9 \ kg$$
  • $$0.9 \ kg$$
  • $$0.5 \ kg$$
A uniformly tapering conical wire is made from a material of Young's modulus $$Y$$ and has a normal, unextended length $$L$$. The radii, at the upper and lower ends of this conical wire, have values $$R$$ and $$3R$$, respectively. The upper end of the wire is fixed to a rigid support and a mass $$M$$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal to:
  • $$L\left( 1+\dfrac { 1 }{ 3 } \dfrac { Mg }{ \pi \Upsilon { R }^{ 2 } } \right) $$
  • $$L\left( 1+\dfrac { 2 }{ 9 } \dfrac { Mg }{ \pi \Upsilon { R }^{ 2 } } \right) $$
  • $$L\left( 1+\dfrac { 1 }{ 9 } \dfrac { Mg }{ \pi \Upsilon { R }^{ 2 } } \right) $$
  • $$L\left( 1+\dfrac { 2 }{ 3 } \dfrac { Mg }{ \pi \Upsilon { R }^{ 2 } } \right) $$
A thin 1 m long rod has a radius of 5 mm.1 A force of 50 $$\pi kN$$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ? 
  • The maximum value of Y that can be determined is $$10^{14} N/m^2$$.
  • $$\frac{\Delta Y}{Y}$$ gets minimum contribution . from the uncertainty in the length.
  • $$\frac{\Delta Y}{Y}$$ gets its maximum contribution from the uncertainty in strain
  • The figure of merit is the largest for the length of the rod.
If speed(V), acceleration(A) and force(F) are considered as fundamental units, the dimension of Young's modulus will be?
  • $$V^{-2}A^2F^2$$
  • $$V^{-4}A^2F$$
  • $$V^{-4}A^{-2}F$$
  • $$V^{-2}A^2F^{-2}$$
A bottle has an opening of radius $$a$$ and length $$b$$. A cork of length $$b$$ and radius $$(a+ \Delta a)$$ where $$(\Delta a << a)$$ is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and the frictional coefficient between the bottle and cork is $$\mu$$ then the force needed to push the cork into the bottle is :
474891.JPG
  • $$(\pi \mu B b)a$$
  • $$(2\pi \mu B b)\Delta a$$
  • $$(\pi \mu B b)\Delta a$$
  • $$(4\pi \mu B b)\Delta a$$
Temperature of a gas is $$20^{0}\mathrm{C}$$ and pressure is changed from $$1.01\times 10^{5}$$ Pa to $$1.165\times 10^5\mathrm{P}\mathrm{a}$$. If volume is decreased isothermally by 10%. The bulk modulus of gas is (in $$Pa$$):
  • $$1.55\times 10^{5}$$
  • $$0.155\times 10^{5}$$
  • $$1.4\times 10^{5}$$
  • $$1.01\times 10^{5}$$
$$\mathrm{A}$$ student performs an experiment to determine the Young's modulus of a wire, exactly 2 $$\mathrm{m}$$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $$0.8 mm$$ with an uncertainty of $$\pm 0.05$$ mm at a load of exactly $$1.0 kg$$. The student also measures the diameter of the wire to be $$0.4 mm$$ with an uncertainty of $$\pm 0.01$$ mm. Take $$\mathrm{g}=9.8\mathrm{m}/\mathrm{s}^{2}$$ (exact). The Young's modulus obtained from the reading is 
  • $$(2.0\pm 0.3)\times 10^{11}\mathrm{N}/\mathrm{m}^{2}$$
  • $$(2.0\pm 0.2)\times 10^{11}\mathrm{N}/\mathrm{m}^{2}$$
  • $$(2.0\pm 0.1)\times 10^{11}\mathrm{N}/\mathrm{m}^{2}$$
  • $$(2.0\pm 0.05)\times 10^{11}\mathrm{N}/\mathrm{m}^{2}$$
Dimensions of stress are :
  • $$[ML^2T^{-2}]$$
  • $$[ML^0T^{-2}]$$
  • $$[ML^{-1}T^{-2}]$$
  • $$[MLT^{-2}]$$
The bulk modulus of a spherical objects is '$$B$$'. If it is subjected to uniform pressure '$$P$$', the fractional decrease in radius is:
  • $$\dfrac{P}{3B}$$
  • $$\dfrac{P}{B}$$
  • $$\dfrac{B}{3P}$$
  • $$\dfrac{3P}{B}$$
Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is $$'\Delta l'$$. Which of the following graph is a straight line?
  • $$\Delta l \, vs \, \dfrac{1}{l}$$
  • $$\Delta l \, vs \, l^2$$
  • $$\Delta l \, vs \,\dfrac {1}{l^2}$$
  • $$\Delta l \, vs \, l$$
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
  • $$Length = 50\ cm, diameter = 0.5\ mm$$
  • $$Length = 100\ cm, diameter = 1\ mm$$
  • $$Length = 200\ cm, diameter = 2\ mm$$
  • $$Length = 300\ cm, diameter = 3\ mm$$
The Young's modulus of steel is twice that of brass. Two wires of sample length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:
  • $$1:1$$
  • $$1:3$$
  • $$2:1$$
  • $$4:1$$
The length of a metal wire is $$l_1$$ when the tension in it is $$T_1$$ and is $$I_2$$ when the tension is $$T_2$$. The natural length of the wire is?
  • $$\dfrac{l_1+l_2}{2}$$
  • $$\sqrt{l_1/I_2}$$
  • $$\dfrac{I_1T_2-I_2T_1}{T_2-T_1}$$
  • $$\dfrac{I_1T_2+l_2T_1}{T_1+T_2}$$
How much force is required to produce an increase of $$0.2\%$$ in the length of a brass wire of diameter $$0.6\ mm$$? (Young's modulus for brass $$= 0.9 \times 10^{11} N / m^2$$) 
  • Nearly $$17\ N$$
  • Nearly $$34\ N$$
  • Nearly $$51\ N$$
  • Nearly $$68\ N$$
Which of the following is an example of elastic deformation?
  • stretching a rubber band
  • stretching salt water taffy
  • both
  • none
The Bulk modulus for an incompressible liquid is :
  • Zero
  • Unity
  • Infinty
  • Between 0 and 1
When a body undergoes a linear tensile strain if experience a lateral contraction also. The ratio of lateral contraction to longitudinal strain is known as
  • Young's modulus
  • Bulk modulus
  • Poisson's law
  • Hooke's law
Which of the following is not dimension less
  • Poission ratio
  • Sharing strain
  • Longitudinal strain
  • Volume stress
A wire suspended vertically from one of its ends is stretched by attaching a weight of $$200N$$ to the lower end. The weight stretches the wire by $$1mm$$. Then the elastic energy stored in the wire is 
  • $$0.2J$$
  • $$10J$$
  • $$20J$$
  • $$0.1J$$
In plastic deformation, deformation is 
  • reversible
  • permanent
  • both
  • none
Out of the following whose elasticity is independent of temperature
  • steel
  • copper
  • Invar steel
  • glass
A wire ($$Y=2\times {10}^{11}N/m$$) has length $$1m$$ and area $$1m{m}^{2}$$. The work required to increased its length by $$2mm$$ is
  • $$400J$$
  • $$40J$$
  • $$0.4J$$
  • $$0.04J$$
The Young's modulus of the material of the wire of length $$L$$ and radius $$r$$ is $$Y{ N }/{ { m }^{ 2 } }$$. If the length is reduced to $${ L }/{ 2 }$$ and radius $${ r }/{ 2 }$$, the Young's modulus will be:
  • $$\dfrac { Y }{ 2 } $$
  • $$Y$$
  • $$2Y$$
  • $$4Y$$
Which of the following is an example of plastic deformation?
  • stretching a rubber band
  • stretching salt water taffy
  • none
  • both
As compared to concrete, steel has compressive strength:
  • $$25$$ times less
  • equal
  • $$25$$ times more
  • $$5$$ times more
Fill in the blank.
In a technical sense a substance with a ________ elasticity is one that requires a ______  force to produce a distortion-for example, a steel sphere. 
  • high, small
  • high, large
  • low, large
  • low , small
Which of the following are close to ideal plastics?
  • Putty
  • Mud
  • Rubber band
  • None of the above
The dimensions of strain is:
  • $$L$$
  • $$L^{2}$$
  • It is dimensionless
  • $$ML^{2}T^{-2}$$
The property to restore the natural shape or to oppose the deformation is called :
  • elasticity
  • plasticity
  • ductility
  • none of the above
The unit of stress is:
  • $$kg$$ $${m}^{-2}$$
  • $$N$$ $${kg}^{-1}$$
  • $$N{m}^{-2}$$
  • $$N$$
The bulk modulus of elasticity with increase in pressure 
  • increases
  • decreases
  • remains constant
  • increases first up to certain limit and then decreases
Linear elastic deformation is governed by ________
  • Hooke's Law
  • Euler Bernoulli's equation
  • both
  • none
A steel cable with a radius $$2cm$$ supports a chairlift at a ski area. If the maximum stress is not to exceed $${ 10 }^{ 8 }N\quad { m }^{ -2 }$$, the maximum load the cable can support is
  • $$4\pi \times { 10 }^{ 5 }N$$
  • $$4\pi \times { 10 }^{ 4 }N$$
  • $$2\pi \times { 10 }^{ 5 }N$$
  • $$2\pi \times { 10 }^{ 4 }N$$
For a perfectly rigid body
  • Young's modulus is infinite and bulk modulus is zero
  • Young's modulus is zero and bulk modulus is infinite
  • Young's modulus is infinite and bulk modulus is also infinite
  • Young's modulus is zero and bulk modulus is also zero
Which of the following statements is incorrect?
  • When a material is under tensile stress, the restoring forces are caused by interatomic attraction while under compressional stress, the restoring force is due to interatomic repulsion
  • The stretching of a coil is determined by its shear modulus
  • Rubber is more elastic than steel
  • Shearing stress plays an important role in the buckling of shafts
The ratio of hydraulic stress to the corresponding strain is known as 
  • Compressibility
  • Bulk modulus
  • Young's modulus
  • Rigidity modulus
  • Expansion coefficient
For an ideal liquid
  • bulk modulus is infinite and shear modulus is zero
  • bulk modulus is zero and shear modulus is infinite
  • bulk modulus is infinite and shear modulus is also infinite
  • bulk modulus is zero and shear modulus is also zero
The Young's modulus of a wire of length $$L$$ and radius $$r$$ is $$Y$$. If the length is reduced to $$\cfrac{L}{2}$$ and radius is $$\cfrac{r}{2}$$, then the Young's modulus will be 
  • $$\cfrac { Y }{ 2 } $$
  • $$Y$$
  • $$2Y$$
  • $$4Y$$
If Poisson's ratio $$\sigma$$ for a material is $$-\dfrac {1}{2}$$, then the material is
  • Elastic fatigue
  • Incompressible
  • Compressible
  • None of the above
The shear modulus is also known as
  • bulk modulus
  • Young's modulus
  • modulus of rigidity
  • Poisson's ratio
A material has Poisson's ratio $$0.5$$. if a uniform rod of it suffers a longitudinal strain of $$2\times {10}^{3}$$, then the percentage change in volume is
  • $$0.6$$
  • $$0.4$$
  • $$0.2$$
  • zero
Longitudinal strain is
  • always positive
  • always negative
  • may be positive or negative
  • zero
Bulk Modulus, Pressure, Force, Stress,  which one of these wont have the same unit as the others?
  • Bulk Modulus
  • Pressure
  • Force
  • Stress
The ratio of lateral strain to the linear strain within elastic limit is known as:
  • Young's modulus
  • Bulk's modulus
  • Rigidity modulus
  • Poisson's ratio
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Both Assertion and Reason are incorrect
A spring is made of steel and not of copper because
  • steel is more elastic than copper
  • steel is less elastic than copper
  • steel is more plastic than copper
  • steel is less plastic than copper
Substances that break just after elastic limit is reached are known as 
  • brittle substances
  • breakable substances
  • ductile substances
  • elastic substances
A wire is stretched to double its length. The strain is :
  • $$infinity$$
  • $$1$$
  • $$zero$$
  • $$0.5$$
0:0:1


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