CBSE Questions for Class 11 Engineering Physics Mechanical Properties Of Solids Quiz 4 - MCQExams.com

In Youngs expt., the distance between two slits is d/3 and the distance between the screen and the slits is 3D. The number of fringes in 1/3 m on the screen, formed by monochromatic light of wavelength $$3\lambda $$, will be? 
  • $$\frac{d}{9D\lambda }$$
  • $$\frac{d}{27D\lambda }$$
  • $$\frac{d}{81D\lambda }$$
  • $$\frac{d}{D\lambda }$$
The Poissons ratio for inert gases is:
  • $$1.40$$
  • $$1.66$$
  • $$1.34$$
  • $$None \ of \ these$$
One end of a string of length L and cross-sectional area A is fixed to a support and the other end is fixed to a bob of mass m. The bob is revolved in a horizontal circle of radius r, with an angular velocity $$\omega $$, such that the string makes an angle $$\theta $$ with the vertical. The increase $$\Delta L$$ in length of the string is
  • $$\dfrac{ML}{AY}$$
  • $$\dfrac{MgL}{AY cos\theta }$$
  • $$\dfrac{MgL}{AY sin\theta }$$
  • $$\dfrac{MgL}{AY}$$
One end of a string of length $$L$$ and cross-sectional area $$A$$ is fixed to a support and the other end is fixed to a bob of mass $$m$$. The bob is revolved in a horizontal circle of radius $$r$$ with an angular velocity $$\omega $$ such that the string makes an angle $$\theta $$ with the vertical. The stress in the string is :
  • $$\dfrac{mg}{A}$$
  • $$\dfrac{mg}{A} \left ( 1-\dfrac{r}{L} \right )$$
  • $$\dfrac{mg}{A} \left ( 1+\dfrac{r}{L} \right )$$
  • none of these

In Young's double slit experiment, the two equally bright slits are coherent, but of phase difference  $$\dfrac{\pi}{3}$$ .If maximum intensity on the screen is$$I_0$$, the intensity at the point on the screen equidistant from the slits is____?
  • $$I_0$$
  • $$\dfrac{I_0}{2}$$
  • $$\dfrac{I_0}{4}$$
  • $$\dfrac{3 I_0}{4}$$

The average depth of Indian Ocean is about 3000 m. Calculate the fractional compression,$$\frac{\Delta V}{V}$$ of water at the bottom of the ocean, given that the bulk modulus of water is $$2.2 \times 10^9Nm^{-2}$$ (consider $$g=10  ms^{-2}$$)
  • 0.82%
  • 0.91%
  • 1.24%
  • 1.36%
Four uniform wires of the same material are stretched by the same force. The dimensions of wire are as given below. The one which has the minimum elongation has :
  • radius $$3\ mm$$, length $$3\ m$$
  • radius $$0.5\  mm$$, length $$0.5\  m$$
  • radius $$2 \ mm$$, length $$2\  m$$
  • radius $$3 \ mm$$, length $$2\  m$$
A rubber ball is brought into 200 m deep water, its volume is decreased by 0.1% then volume  elasticity coefficient of the material of ball will be:
$$(Given\ \rho = 10^3 kg/m^3$$ and $$ g = 9.8 ms^{-2})$$
  • $$19.6 \times 10^8 N/m^2$$
  • $$19.6 \times 10^{-10} N/m^2$$
  • $$19.6 \times 10^{10} N/m^2$$
  • $$19.6 \times 10^{-8} N/m^2$$
(i) For a Searle's experiment, in the graph shown, there are two readings a and b that are not lying on the straight line
(ii) Experiment is not performed precisely

120016.jpg
  • Both (i) and (ii) are true and (ii) is reason for (i)
  • Both (i) and (ii) are true but (ii) is not reason for (i)
  • Only (i) is true
  • Only (ii) is true
The velocity of sound in glass in0m/sec, it's density is 2,927 gm c.c. Calculate Youngs modules of glass in dynes/cm$$^{2}$$
  • $$65 \times 10^{12}$$
  • $$65 \times 10^{16}$$
  • $$73.17 \times 10^{9} $$
  • $$65 \times 10^{11}$$
A sample of a liquid has an initial volume of $$1.5 L$$. The volume is reduced by $$0.2 mL,$$ when the pressure increases by $$140 kPa$$. What is the bulk modulus of the liquid.
  • $$1.05 \times 10^{9}$$ Pa
  • $$1.05 \times 10^{5}$$ Pa
  • $$3.05 \times 10^{9}$$ Pa
  • $$3.05 \times 10^{5}$$ Pa
Velocity of sound, (Y) youngs modules, and p density of solid are related as
  • $$v=\sqrt{Y p}$$
  • $$v=\sqrt{Y/p}$$
  • $$v^2 = Yp$$
  • Both (a) and (b)
A spherical ball is compressed by $$0.01$$% when a pressure of $$100 $$ atmosphere is applied on it. Its bulk modulus of elasticity in $$dyne/cm^{2}$$ will be approximately
  • $$10^{12}$$
  • $$10^{14}$$
  • $$10^{6}$$
  • $$10^{24}$$
(i) In Searle's experiment, after every step of loading, one waits for sometime (2 or 3 min) before taking reading.
(ii) In this duration, the wire becomes free from kinks.
  • Both (i) and (ii) are true and (ii) is reason for (i)
  • Both (i) and (ii) are true but (ii) is not reason for (i)
  • Only (i) is true
  • Only (ii) is true
The modulus of elasticity of a material does not depend upon
  • shape
  • temperature
  • nature of material
  • impurities mixed
The ratio of change in dimension at right angles to applied force to the initial dimension is defined as
  • $$Y$$
  • $$\eta$$
  • $$\beta$$
  • $$K$$
A wire is stretched through $$1 mm$$ by certain load. The extension produced in the wire of same material with double the length and radius will be
  • $$4 mm$$
  • $$3 mm$$
  • $$1 mm$$
  • $$0.5 mm$$
Two identical wires of different materials have Young's moduli of elasticity as $$22\times10^{10}N/m^2$$ and $$11\times10^{10}N/m^2$$ respectively. If these are stretched by equal loads then the ratio of extensions produced in them will be:
  • 2 : 1
  • 1 : 2
  • 4 : 1
  • 1 : 4
Which of the following pairs is not correct?
  • strain-dimensionless
  • stress-$$N/m^{2}$$
  • modulus of elasticity-$$N/m^{2}$$
  • poisson's ratio-$$N/m^{2}$$
Equal weights are suspended from the wires of same material and same lengths but with radii in the ratio $$1 : 2$$. The ratio of extensions produced in them will be
  • $$4 : 1$$
  • $$1 : 4$$
  • $$1 : 2$$
  • $$2 : 1$$
The modulus of elasticity at constant temperature is
  • $$\gamma P$$
  • $$\frac{P}{\gamma}$$
  • $$P$$
  • $$\frac{P}{V}$$
A stress of $$2\ kg/mm^{2}$$ is applied on a wire. If $$Y=10^{12}\ dyne/cm^2$$ then the percentage increase in its length will be
  • $$0.196\%$$
  • $$19.6\%$$
  • $$1.96\%$$
  • $$0.0196\%$$
The expression for the determination of Poisson's ratio for rubber is
  • $$\displaystyle \sigma=\frac{1}{2}\left[1-\frac{dV}{AdL}\right]$$
  • $$\displaystyle \sigma=\frac{1}{2}\left[1+\frac{dV}{AdL}\right]$$
  • $$\displaystyle \sigma=\frac{1}{2}\frac{dV}{AdL}$$
  • $$\displaystyle \sigma=\frac{dV}{AdL}$$
A $$10 \ meter$$ long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be :$$(Y=5\times10^{6}N/m^{2}$$ and density of rubber =$$ 1500 \ kg/m^{3}$$)
  • $$1.5\  m$$
  • $$0.15\  m$$
  • $$0.015 \ m$$
  • $$0.0015 \ m$$
Two identical wires are suspended from a roof, but one is of copper and other is of iron. Young's modulus of iron is thrice that of copper. The weights to be added on copper and iron wires so that the ends are on the same level must be in the ratio of
  • 1 : 3
  • 2 : 1
  • 3 : 1
  • 4 : 1
For a material $$\sigma=-0.25$$ under an external stress, the longitudinal strain is $$10^{-2}$$. The percentage change in the diameter of the wire is
  • $$+1$$%
  • $$-1$$%
  • $$+0.25$$%
  • $$-0.25$$%
A wire of density $$9\times10\space kg\space m^{-3}$$ stretched between two clamps $$1\space m$$ apart is subjected to an extension of $$4.9\times10^{-4}\space m$$. If Young's modulus of the wire is $$9\times10^{-4}\space m$$. The lowest frequency of transverse vibrations in the wire is
  • $$35\space Hz$$
  • $$70\space Hz$$
  • $$105\space Hz$$
  • $$140\space Hz$$
A wire made of the material of Young's modulus $$Y$$ has an stress $$S$$ applied to it. If Poisson's ratio of the wire is $$\sigma$$, the lateral strain is:
  • $$\displaystyle \sigma\frac{S}{Y}$$
  • $$\displaystyle \sigma\frac{Y}{S}$$
  • $$\displaystyle \sigma Y\times S$$
  • $$\displaystyle \frac{S}{\sigma Y}$$
A steel girder can bear a load of $$20 tons$$. If the thickness of girder is double, then for the same depression it can bear a load of :
  • 40 ton
  • 80 ton
  • 160 ton
  • 5 ton
A spiral spring is stretched by a weight attached to it. The strain is
  • shear
  • elastic
  • tensile
  • bulk
A gas undergoes a process in which its pressure P and volume V are related as $$VP^n=$$ constant. The bulk modulus for the gas in this process is:
  • np
  • p$$^{1/n}$$
  • $$\dfrac{p}{n}$$
  • p$$^n$$
A vertical steel post of diameter $$25 cm$$ and length $$2.5 m$$ supports a weight of $$8000 kg$$. Find the change in length produced.
(Given $$Y=2\times 10^{11}Pa$$)
  • 2.1 cm
  • 0.21 cm
  • 0.21 mm
  • 0.021 mm
Which one of the following substance possesses the highest elasticity?
  • rubber
  • glass
  • steel
  • copper
A spiral spring is stretched to 20.5 cm gradation on a metre scale when loaded with a 100 g load and to the 23.3 cm gradation by 200 g load. The spring is used to support a lump of metal in air and the reading now is 24.0 cm. The mass of metal lump is :
  • 250 gm
  • 225 gm
  • 145 gm
  • 750 gm
A petite young woman of $$50\ kg$$ distributes her weight equally over her high-heeled shoes. Each heel has an area of $$0.75cm^2$$. Find the pressure exerted by each heel? Take $$g=10 m/s^2$$
  • $$6.66\times10^{6}Pa$$
  • $$3.33\times10^{6}Pa$$
  • $$1.67\times10^{6}Pa$$
  • $$4.44\times10^{6}Pa$$
A stone of mass m tied to one end of a thread of length l. The diameter of the thread is d and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle $$\theta$$ with the vertical. Find the increase in length of the wire. Young's modulus of the wire is Y.
  • $$\displaystyle \frac{4mgl}{\pi d^{2}Y\cos\theta}$$
  • $$\displaystyle \frac{4mgl}{\pi d^{2}Y\sin\theta}$$
  • $$\displaystyle \frac{4mgl}{\pi d^{2}Y}$$
  • $$\displaystyle \frac{4mgl}{\pi d^{2}Y\sec\theta}$$
Outside a house, $$1 km$$ from ground zero of a $$100 $$ kiloton nuclear bomb explosion, the pressure will rapidly rise to as high as $$2.8$$ atm while the pressure inside the house is $$1$$ atm. If the area outside the house is $$50\:m^2$$. The resulting net force exerted by the air in front of the house is :
  • $$9.1\times10^{6}N$$
  • $$2.1\times10^{7}N$$
  • $$1.41\times10^{7}N$$
  • $$1.63\times10^{7}N$$

A uniform heavy rod of length $$L$$, weight $$W$$ and cross-sectional area $$A$$ is hanging from a fixed support. Young's modulus of the material is $$Y$$. Find the elongation of the rod.


143517.png
  • $$\displaystyle \dfrac{WL}{AY}$$
  • $$\displaystyle \dfrac{WL}{2AY}$$
  • $$\displaystyle \dfrac{WL}{4AY}$$
  • $$\displaystyle \dfrac{WL}{3AY}$$
Poisson's ratio cannot exceed
  • 0.25
  • 1.0
  • 0.75
  • 0.5
A student plots graph from his readings on the determination of Young's modulus of a metal wire but forgets to put the labels (figure). The quantities on $$X$$ and $$Y$$-axes respectively may be

142671_d2101415dc914c9ea498d5c4fad77c00.png
  • weight hung and length increased.
  • stress applied and length increased.
  • stress applied and strain developed.
  • length increased and the weight hung
The length of a wire is $$l_1$$ when tension is $$T_1$$ and $$l_2$$ when tension is $$T_2$$. The natural length of the wire is
  • $$\displaystyle \frac{l_1+l_2}{2}$$
  • $$\sqrt{l_1l_2}$$
  • $$\displaystyle \frac{l_1T_2-l_2T_1}{T_2-T_1}$$
  • $$\displaystyle \frac{l_1T_2+l_2T_1}{T_2+T_1}$$
  • $$\displaystyle \frac{l_1T_1-l_2T_2}{T_1-T_2}$$
A sphere of mass M kg is suspended by a metal wire of length L and diameter d. When in equilibrium, there is a gap of $$\Delta l$$ between the sphere and the floor. The sphere is gently pushed aside so that it makes an angle $$\theta$$ with the vertical. Find $$\theta_{max}$$ so that sphere fails to rub the Floor, Young's modulus of the wire is Y.

143823_3646dfd2f2654eacac6070f61f802600.png
  • $$\displaystyle \sin^{-1}\left(1-\frac{Y\pi d^{2}\Delta l}{8MgL}\right)$$
  • $$\displaystyle \tan^{-1}\left(1-\frac{Y\pi d^{2}\Delta l}{8MgL}\right)$$
  • $$\displaystyle \cos^{-1}\left(1-\frac{Y\pi d^{2}\Delta l}{8MgL}\right)$$
  • none
A copper wire of cross-section A is under a tension T. Find the decrease in the cross-section area. Young's modulus is Y and Poisson's ratio is $$\sigma$$
  • $$\displaystyle \frac{\sigma T}{2AY}$$
  • $$\displaystyle \frac{\sigma T}{AY}$$
  • $$\displaystyle \frac{2\sigma T}{AY}$$
  • $$\displaystyle \frac{4\sigma T}{AY}$$
Two wires of the same material and length are stretched by the same force. Their masses are in the ratio $$3 : 2$$. Their elongations are in the ratio
  • $$3 : 2$$
  • $$9 : 4$$
  • $$2 : 3$$
  • $$4 : 9$$
Two identical wires of iron and copper with their Young's modulus in the ratio $$3:1$$ are suspended at same level. They are to be loaded so as to have the same extension and hence level. Ratio of the weight is
  • $$1:3$$
  • $$2:1$$
  • $$3:1$$
  • $$4:1$$
The length of a wire is increased by $$1\ mm$$ on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is
  • $$0.25\ mm$$
  • $$0.5\ mm$$
  • $$2\ mm$$
  • $$4\ mm$$
Young's modulus of rubber is $$10^{4} N/m^{2}$$ and area of cross section is $$2\ cm^{-2}$$. If force of $$2\times 10^{5}$$ dyn is applied along its length, then its initial $$l$$ becomes.
  • $$3l$$
  • $$4l$$
  • $$2l$$
  • None of these
A cube is shifted to a depth of $$100m$$ is alake. The change in volume is $$0.1$$%. The bulk modules of the material is nearly
  • $$10Pa$$
  • $${10}^{4}Pa$$
  • $${10}^{7}Pa$$
  • $${10}^{9}Pa$$
Two wires of the same length and same material but radii in the ratio of $$1:2$$ are stretched by unequal forces to produce equal elongation. The ratio of the two forces is
  • $$1:1$$
  • $$1:2$$
  • $$1:3$$
  • $$1:4$$
A long wire hangs vertically with its upper end clamped. A torque of $$8\ Nm$$ applied to the free end twists it through $$45^{\circ}$$. The potential energy of the twisted wire is
  • $$\pi J$$
  • $$\dfrac {\pi}{2} J$$
  • $$\dfrac {\pi}{4} J$$
  • $$\dfrac {\pi}{8} J$$
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