Properties of matter Questions and Answers

A uniformly tapering circular bar has its diameter ranging from D a to D a along its length L The bar is subjected to an axial force P and young s modulus is Y The percentage error in the calculation of elongation of bar if mean diameter is used in calculation instead of actual diameter 2a A 100 D C a 10D B D 102 D a x 100

Two ends of a plank are placed on two wedges The plank gets depressed by 1 mm when a load of 2 kg is hung from its mid point What will be the depression of the plank if 2 5 mm a load of 5 kg is hung from its mid point

The basic reason of the force of surface tension is the tendency of the surface of a liquid to a Contract c maintain its area expand or contract 1 Point Option a Option b Option C Option d b expand d either to

Two metal rods are fixed end to end between two rigid supports as shown in figure Each rod has length L and area of cross section is A When the system is heated up the junction between the rods does not shift y and y are young s modulus of materials o rods a and a are coefficients of linear expansion Find the value of THE M L a Y L a Y y 02 ROUP

Each atom of an iron bar 5cmx1cmx1cm has a magnetic moment 1 8x10 2A m What will be the magnetic moment of bar in the state of magnetic saturation in A m Density of iron 7 78 10 kg m Atomic weight of iron A 58 Avogadro number M 602 10 3 mol

20 Refrigerator is to maintain eatables kept inside at 7 C If the room temperature is 43 C coefficient of performance of refrigerator must be NCERT Pg 322 1 7 78 2 13 7 3 9 72 4 0 75

Three thin wires of equal length are suspended from the top of a roof The respective ratio of their area of cross section is 1 2 4 and Young s modulii is 4 2 1 then the ratio of their weights to be attached at the other ends to obtain same elongation in them is

hermal Properties of Matter Board Competitive Exams Coefficient of volume expansion of mercury is 0 18 x 10 PC If the density of mercury at 0 C is 13 6 g cc then its density at 200 C is 1 13 11 g cc m 16 11 pics 2 52 11 g cc 4 26 11 gior

4 Almost independent of h 9 A spring balance reads 200 gF when carrying a lump of lead in air If the lead is now immersed with half of its volume in brine solution what will be the new reading of the spring balance specific gravity of lead and brine are 11 4 and 1 1 respectively 1 190 4 gF 2 180 4 g

A force F is applied along a rod of transverse cross sectional area A The tangential stress to a section PQ inclined at an angle 0 to transverse section will be maximum for angle 0 in degree is 1 O 3 45 FO FL 0 C P OF 2 30 4 90

cm 3 6 cm 4 8 cm The pressure at the bottom of a water tank is 4 P where P is atmospheric pressure If water is drawn out till the water level decreases by th then 3 pressure at the bottom of the tank is 21 3 P 8 11P 2 7 P 6 9 P

REVIEW EXERCISES 1 43 Define point defects in solids 1 44 What is Schottky defect 1 45 What is the effect of the presence of Schottky defects on the density of a crystal 46 What are interstitials in a crystal 1 47 Pure silicon does not conduct electricity How can it be made a conductor of electricity Explain with examples

A To minimise the depression in a beam it is designed as T shape girder R The T shape girders have large load bearing surface which decreases the stress

1 When a force is applied on a wire of uniform cross sectional area 3 x 10 m and length 4 m the increase in length is 1 mm Energy stored in it will be Y 2 x 10 N m 1 6250 J 3 0 075 J 2 0 177 J 4 0 150 J

decreases A Spring balances show wrong readings after they have been used for a long time R Spring in spring balance temporary losses elasticity due to repeated alternating deforming

of the body A Adiabatic elasticity of a gas is greater than isothermal elasticity Eadiabatic R

The dual nature of light is exhibited by O Photoelectric effect O Refraction and interference O Diffraction and reflection hr

4 3 2 Y 4r Y 9 A cube of side 40 mm has its upper face displace by 0 1 mm by a tangential force of 8 kN TH shearing modulus of cube is 2 4x 10 Nm 2 1 2 x 10 Nm

4 9 8 x 10 N m A mild steel wire of length 2 meter cross sectional area A m is fixed horizontally between two pillars A small mass m kg is suspended from the mid point of the wire If extension in wire are within elastic limit Then depression at the mid point of wire will be 1 3 1 M9 Mg 3 4 Mg IA Mgl YA Mg 2YA 1 3 1 3

52 3 5 4 0 When a uniform metallic wire is stretched the lateral strain produced in it is If a and Y are the Poisson s ratio and Young s modulus for wire then elastic potential energy density of wire is E YB 2 Ya 2 YB 20 Yo

Two parallel and opposite forces each 4000 N are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side Find the angle of shear and the displacement of the upper surface relative to the lower surface The shear modulus for the metal is 80 GPa 90 a 0 2 x 10 6 cm c 2 65 x 10 5 cm b 2 0 x 105 cm 2014021 d 2 15 x 105 cm

7 Stress strain curve for four metals are shown in figure The maximum young modulus of elasticity is for meta Strain 1 A 3 C Stress 2 B 4 D

You do a very precise experiment to test the properties of a piece of wire You stretch the wire by applying an outward force to each end of the wire and measure its change in length If you then precisely double this force and the wire still remains elastic but is beyond proportionality limit the change in length of the wire 1 will exactly double 49 2 will just slightly more than double 3 will just slightly less than double 4 will decrease by exactly a factor of two

Al Arrangement of three metallic rods riveted to each other is as shown in figure a is the coefficient of linear expansion for aluminum and a when a ag for steel The arrangement is heated then Al Steel AI Steel 52 1 Tensile stress is developed in the aluminum rod 2 Compressive stress is developed in the aluminum rod 3 No stress is developed in the aluminum rod 4 Data s are incomplete to decide

If internal energy U of an ideal gas depends on pressure p and volume V of the gas according to equation U 3pV which of the following conclusions can you make regarding the gas a The gas is not a mono atomic gas b The gas can be a di atomic gas c The gas can be a tri atomic gas d Molar specific hoot

4 None of these 31 Two vessel of the same volume contain the 31 same gas at same temperature If pressure in the vessel are in ratio of 1 2 then 1 Ratio of v is 1 2 rms 2 Ratio of average kinetic energy is 1 1 3 Ratio of average velocity is 1 2 4 Ratio of number of molecules is 1 2 4 473 474 1 v 2 a 3 a 4 1 2 1 2 1 2 1

O Single Correct MCQ An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm What will be length of the air column above mercury in the tube now Atmospheric pressure is 76 cm of Hg A B C 38 cm 6 cm 16 cm

4 A human body has a surface area of approximately 1 m The normal body temperature is 10 K above the surrounding room temperature To Take the room temperature to be To 300 K For To 300 K the value of o 460 Wm 2 where o is the Stefan Boltzmann constant Which of the following options is are correct A The amount of energy radiated by the body in 1 second is close to 60 Joules B If the surrounding temperature reduces by a small amount AT To then to maintain the same body temperature the same living human being needs to radiate AW 40T3ATO more energy per unit time C Reducing the exposed surface area of the body e g by curling up allows humans to maintain the same body temperature while reducing the energy lost by radiation D If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths

If 5 of the energy supplied to a bulb is radiated as visible light how many photons are emitted per second by 100 watt lamp Wavelength c visible light taken is 5 6 x 10 7 m 1 4 1019 1 9 1016 3 4 1020

06 A bar produces a lateral strain of magnitude 60 x 10 5 m m when subjected to tensile stress of magnitude 300 MPa along the axial direction What is the elastic modulus of the material if the Poisson s ratio is 0 3 a 100 GPa c 200 GPa b 150 GPa d 400 GPa

105 The temperature of a steel rod placed between rigid supports and of length L area of cross section A Young s Modulus Y and coefficient of linear expansion a is raised by T The amount of work done when heated is a L s a as at a 45 45 rog o A do Min ro boards dd Joesos 2005 30 35 YAG T L 2 YA QIL 2 Y do 298 fatia og dod 00 T 3 YA a T 4 YAaT L

Figure shows an ideal spring block system force constant of spring is k which has been compressed by an amount Xo If x is instantaneous deflection of spring from its natural length mark the correct options vooooo m Smooth A Instantaneous power delivered by spring is k kx 2 x x 2m

111 If E G and K denote the young s modulus modulus of rigidity and bulk modulus for an elastic material then which one of the followings can be possibly true a G 2K c K E b G E d G K E Engg Services 205

Steel ruptures when a shear of 3 5 x 108 Nm 2 is applied The force needed to punch a 1 cm diameter hole in a steel sheet 0 3 cm thick is nearly Question Type Single Correct Type 1 2 3 4 3 3 104 N 1 4 104 N 1 1 104 N 2 7 x 104 N

18 A uniform cylindrical rod of length L cross section and Young s modulus Y is acted upon by the forces as shown in figure The elongation of the rod is 1 3 3F 2 F 5 AY 3 F 2 F co r 3 F 5 AY 8 F 2F roid

3 Young s A uniform heavy rope of weight W sectional area A is hanging from rigid support It Young s modulus of material is Y then strain is W 1 4 AY 2 W AY JA

0 45 B 2 A long elastic cord obeying Hooke s law is stretched considerably due to its own weight In one such case a cord is held from one of its ends and hung vertically and in another case that is shown in the figure the ends are attached to separate nails A and B in the same level so that the cord assume shape of a catenary In which case is the cord stretched longer

11 The thermal stress developed in the rod by rigid supports as shown F Rigid Support Rod 1 Directly proportional to its length 2 Inversely proportional to its area of cross section 3 Directly proportional to its area of cross section

Q10 A uniform pressure of 7 0x105 N m is applied to all six sides of a copper cube What is the percentage change in volume of the cube for copper B 14x100 N O A 2 4 x 10 2 O B 0 4 x 10 10 2 00

Q1 A uniform pressure of 7 0x105 N m is applied to all six sides of a copper cube What is the percentage change in volume of the cube for copper B 14x100 N mm O A 0 4 x 10 2 O B 0 5 x 10 3 O C 24 x 10 2 O D 8 4 x 10 2

Q7 Young s modulus of a material is defined as ratio of stress and strain If strain of the material is increases by two times the Young s modulus of the mater O A Increases by two times B No change in the Young s Modulus C Decreases by two times O D Increases by four times

7 A rod of length 1000 mm and coefficient of linear expansion a 104 C is placed symmetrically between two fixed supports separated by 1001 mm The Young s modulus of the rod is 10 N m If the temperature is increased by 20 C then the stress developed in the rod is 1000 mm 1001 mm 1 10 N m 3 10 N m 2 10 N m 4 10 N m

3 2 The youngs modulus of a rubber string 8 cm long and density 1 5 kg m is 5 x 108 Nm2 is suspended on the ceiling in a room The increase in length due to its own weight will be 1 9 6 106 m 2 9 6 10 m 39 6 x 10 11 m 4 9 6 cm platform is suspended 1

For the following figure calculate the shear stress V when x 16 0 m Draw the Shear Force and Bending Moment diagrams and upload these at the end of the exam Remember to correctly place the positive or negative sign and highlight the value of the absolute maximum shear force the maximum positive and negative bending moments 7 0 kN m 16 m 4 m X

Mechanical Properties of Solids 13 The edge of an aluminum cube is 10 cm One face of the cube is firmly fixed to a vertical wall A mass of 100 kg is attached to the opposite face of the cube The vertical deflection of this face is G 25 10 Pa NCERT XI Pg 248 2 3 x 10 6 m 1 4 x 10 7 m 3 2 x 10 6 m 4 1 x 10 6 m 14 A rigid bar of mass 15 kg is supported symmetrically by three wires each 2 0 m long Those at each end are of copper and the middle one is of iron If tension in each rod is same the ratio of diameters is nearly NCERT XI Pg 248 2 0 8 1 6 3 4 2 4 2 0 15 The density of water at a depth where pressure is 80 0 atm Given density at the surface is 1 03 x 103 kg m B 2 2 x 10 N m NCERT XI Pg 248 1 1 034 x 10 kg m 2 1 34 x 10 kg m 3 1 64 x 10 kg m 4 2 084 x 103 kg m 16 A rod of length 1 05 m having negligible mass is supported at its ends by two wires of steel wire A and aluminum wire B of equal lengths as shown in figure The cross sectional areas of wire A and B are 2 0 mm and 4 0 mm respectively The distance x from left end where a mass mis suspended in order to produce equal stresses is Yout 2x1011 N m 2 You 7x1010 N m 2 m B NCERT XI Pg 249 1 70 cm 2 35 cm 3 65 cm 4 40 cm 17 In Q16 the distance x from left end to produce equal strains is NCERT XI Pg 249 1 70 cm 2 43 2 cm 3 65 cm 4 35 cm 18 A 15 kg mass fastened to the end of a steel wire of unstretched length 1 0 m is whirled in a vertical circle with an angular velocity of 4 radian s at the bottom of the circle The cross sectional area of the wire is 0 065 cm The elongation of the wire when the mass is at the lowest point is g 10 m s NCERT XI Pg 248 2 2 05 mm 1 1 93 mm 3 1 65 mm 4 3 05 mm 19 A mild steel wire of length 2L and cross sectional area A is stretched within elastic limit horizontally between two pillars as shown in the figure A mass m is suspended from the mid point of the wire Strain in the wine in

The edge of an aluminum cube is 10 cm One face of the cube is firmly fixed to a vertical wall A mass of 100 kg is attached to the opposite face of the cube The vertical deflection of this face is G 25 10 Pa NCERT XI Pg 248 2 3 x 10 6 m 1 4 x 10 7 m 3 2 x 10 6 m 4 1 x 10 6 m 14 A rigid bar of mass 15 kg is supported symmetrically by three wires each 2 0 m long Those at each end are of copper and the middle one is of iron If tension in each rod is same the ratio of diameters is nearly NCERT XI Pg 248 2 0 8 1 6 3 4 2 4 2 0 15 The density of water at a depth where pressure is 80 0 atm Given density at the surface is 1 03 x 10 kg m B 2 2 10 N m NCERT XI Pg 248 1 1 034 10 kg m 2 1 34 10 kg m 3 1 64 x 10 kg m 4 2 084 10 kg m 16 A rod of length 1 05 m having negligible mass is supported at its ends by two wires of steel wire A and aluminum wire B of equal lengths as shown in figure The cross sectional areas of wire A and B are 2 0 mm and 4 0 mm respectively The distance x from left end where a mass m is suspended in order to produce equal stresses is 18 A 19 m NCERT XI Pg 249 1 70 cm 2 35 cm 3 65 cm 4 40 cm 17 In Q16 the distance x from left end to produce equal strains is B NCERT XI Pg 249 2 43 2 cm 1 70 cm 3 65 cm 4 35 cm A 15 kg mass fastened to the end of a steel wire of unstretched length 1 0 m is whirled in a vertical circle with an angular velocity of 4 radian s at the bottom of the circle The cross sectional area of the wire is 0 065 cm The elongation of the wire when the mass is at the lowest point is g 10 m s NCERT XI Pg 248 2 2 05 mm 1 1 93 mm 3 1 65 mm 4 3 05 mm A mild steel wire of length 2L and cross sectional area A is stretched within elastic limit horizontally between two pillars as shown in the figure A mass m is suspended from the mid point of the wir Strain in the 20

Torque of Viscous Forces on a Disc Figure shows a disc D of diameter d connected to an axle placed on a fixed horizontal surface There exist a thin layer of a lubricant of viscosity n between disc and ground of thickness t Find the external torque required to rotate the disc at a uniform angular velocity 0 t D 4

The round weightless bar in the figure is in in diameter E 30 106 psi The applied load is 5700 lbf Find the tensile stress in t bar and the deformation caused by the applied load 2 0 ft The tensile stress in the bar is psi The deformation caused by the applied load is applied load x 10 3 X in

If the light of wavelength is incident on metal surface the ejected fastest electron has speed v If 3 the wavelength is changed to the speed of the 4 fastest emitted electron will be 1 Smaller than 3 2v 4 3 2 Greater than 4 Zero 4 3

Q 27 A U tube having uniform cross section but unequal arm length 1 rm length 1 100 cm and 1 50 cm has same liquid of density p filled in it upto a height h 30 cm as shown in figure Another liquid of density P2 2p is poured in arm A Both liquids are immiscible The length of the second liquid is in cm should be poured in A so that second overtone of A is in unison with fundamental tone of B Neglect end correction A h P14 B