Properties of matter Questions and Answers

A block of mass M area of cross section A and length is placed on smooth horizontal floor Two forces F 5N and F 3 N are applied on the block as shown in the figure If Y is Young s modulus of elasticity of material then total extension in the length of the block will be Area A O 81 AY O2l AY O 41 O AY 5l F 3N Area A F 5N

The length of an elastic string is X m when the tension is 8N and Y m wh the tension is 10 N The length in metres when the tension is 18 N is A 4X 5Y B5Y 4X C 9X 4Y 4Y 9X

A rope of length L is kept along x axis such that its one end is at the origion as shown in the figure An external force is applied on rope such that restoring force developed in the rope is given by Fo 1 where Fo is constant The young s modulus of the rope is given by Yo 1 and cross sectional area is A0 1 where Yo and Ao are constant T 1 elongation in the rope is Al mm and elastic potential energy stored in the rope is joule It is given that Fo 1 kN Yo 2 10 N m Ao 5 mm and L 1 m L The value of Al is X

A plate of mass m and cross sectional area A is moved through a room in which a uniform cloud of dust particles is moving with a velocity v The particle is being acted by an external force F All the particles meeting the plate attach to it Given density of dust p Find the mass and velocity of plate as functions of time the plate is initially at rest F

A cylindrical string is used in guitar The string is to be made of 11 0 g and density of string is 5 x 10 kg m The string ca withstand a breaking stress 14 x 106 N m String can be used under a tension of 44 newton without breaking A stationary wave is formed on the guitar string Now choose the correct option s Length and radius of the longest and thinest string are 70 cm and 1 mm respectively Length and radius of the shortest and thickest string are 70 cm and 1 mm respectively When the standing wave is formed in the guitar string then the particle of the string at the maximum displacement from mean position have maximum potential energy The frequency of the fourth overtone formed in the guitar string is 189 Hz approximately

A Searle s experiment a wire of diameter d 0 060 cm is used to find its young s modulus The length of given wire is L 200 cm and when weight of mass m 30 0 Es used in experiment extension in the length of wire was found to be 0 200 cm Then choose the correct option s Maximum permissible error in young s modulus of wire is 4 66 Maximum permissible error in young s modulus of wire is 3 The least count of the instrument by which length of the wire is to be measured is 1 cm The least count of the instrument by which diameter of the wire is to be measured is 0 001 cm

A light rod is suspended by two elastic strings as shown in the figure A block of mass m is hung at distance from end A such that rod remains horizontal Young s modulus and area of cross section of rods are given in the diagram Find the value of n n Y 2A 2Y A

surface of liquid has spherical shape of radius of curvature R Now sa iquid is placed in a large spherical glass container of radius R If surface iquid container in spherical container is found to be flat then choose the corr alternative s R A A Angle of contact of liquid glass pair is cos C Height h is Ro R B Angle of contact of liquid glass pair is cos R R D Height h is Ro R Ro R O B Ro R R

A and Al are the elongation of wire 1 and 2 respectively due to weigh AL 44 2 d then find the value of 2Y A 2L Symbol have their usual meanings 2 T Y A L

A uniform rod of mass M and length L is hanging freely from a roof as shown B is the mid point of rod If SA SB are the stress on rod at A and B and P P are the strain in the portion AB and BC respectively the choose the correct statement A SA SB C P P L N 2 1 2 A M 2 B M 2 C Rod M L B SA SB D P P

Calculate the force required to punch a hole of 30 mm diameter in a metal plate of 20 mm thickness The permissible shear stress in the material and corresponding factor of safety is 400 MPa and 3 respectively

A wire length L area of cross section A is hanging from a fixed support The len gth of the wire changes to L1 when ma ss M is suspend from its free end The expression for Young s modulus i 2 S

71 A 500 watt bulb is placed at the centre of a perfectly black sphere of radius R 1 metre The approximate pressure experienced by the walls of the sphere as it absorbs all the photon emited by the bulb is take 4 12 6 1 1 3 x 10 7 N m 2 2 5 x 10 7 N m 3 6 3 x 10 7 N m 4 3 14 x 10 7 N m

A bottle has an opening of radius a and length b A cork of length b and radius a Aa where Aa a is compressed to fit into the opening completely see figure If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is u then the force needed to push the cork into the bottle is a b MARKS

A bar made of material whose Young s modulus is equal to E and Poisson s ratio to u is subjected to the hydrostatic pressure p Find the relationship between the compressibility and the elastic constants E and

stic potential energy 1 An iron bar of length L cross section A and Young s modulus Y is pulled by a force F from both the ends so as to produce an elongation e The elastic energy stored in the deformed rod will be 1 3 F L AY F 2A Y 2 F L 2AY 4 None of these

Area A Y Area 2A 2Y L Massless rod At what position should a mass m be suspended on the massless rod so as to produce 1 equal stress in both the wires 2 equal strain in both the wires

A metallic wire is stretched by suspending weight to it If a is the longitudinal strain and is its Young s modulus of elasticity the elastic potential energy per unit volume is given by 01 22a O 11 12a 2 2 1 30

Here graph is plotted between stress and strain for two wire A and B made of different material Select the correct statement on the basis of graph given Young s modulus of wire A is greater it is more brittle stress A A B strain

Two spherical balls of radius 2r and r both having density o are tied up with light string and released in a viscous fluid of density po with the rope just taut The tension in rope when spheres attain terminal velocity 25

The radius of a sphere is found to have reduced by 0 01 when measured at a depth H of sea If the bulk modulus of elasticity of the material of sphere is 4 100 m and density of water is 1000kg m find the value of H use g 10 m s Options 1 2 3 1000 m 1200 m 2000 m 400 m

5 A thin soap film is attached to a light rod in a massless frame as shown in the figure if the length of the rod is 50cm and the surface tension of soap is 0 03 N m if a block of mass 6 grams is attached to the rod using a light string find a Initial acceleration of the block b Increase in surface energy of the film in the first second just after releasing the block 7 5 m s 0 112 J 40cm 2 b 5 m s 0 075 J 50cm m c 2 5 m s 0 112 J d none

Two wires of equal cross sectional area and length L and 2L are suspended as shown in figure Their Young s modulli are Y and Y respectively The equivalent Young s modulli will be 2 1 3 3Y Y 2Y Y Y Y 2 2L 2 4 3Y Y Y 2Y 3Y Y 2 Y Y

Q8 Define stress What is the SI unit of stress Consider two metallic wires P and Q of the same length and material The area of the cross section of wire Q is twice as that of P If they are stretched by the same load find the ratio of stress on wire P and Q 5

Two identical rods P and Q each of cross sectional area A length L and Young s modulus Y are placed on smooth horizontal surface They are acted by horizontal forces as shown below P 2F F Q F

2 58 In producing chlorine through electrolysis 100 W power at 125 V is being consumed How much chlorine per min is liberated ECE of chlorine is 0 367 10 6 kg C AIPMT Prelims 2006 1 17 6 mg 3 24 3 ma 2 21 3 mg 4 13 6 ma

By inserting a capillary tube upito a depth I in water the water rises to a heighth above the surface of the lower end of the copillary is closed inside water the capillary s taken out then the lower end is opened to what height the wetter will remain 2 3 200 1 h 19h

want to use a steel cable to tow your car m 2400 kg The cable is solid steel with a length of 13 m and diameter of 3 cm If you are pulling the car such that its acceleration is 4 m s2 how much will the cable stretc

Two thin wires A and B of equal length L and equal cross sectional area A and masses M and M respectively are joined end to end and suspended as shown in the figure Wires A and B have Young s modulus Y and Y respectively The total elongation in the combined wire is 1 2 3 1 A B M Y2 M Y 2Y gL 2AY Y2 M Y M Y gL AY Y 2M Y2 M Y gL AY Y2 M M Y M Y lgL

5 A drop of olive oil of radius 0 25mm spreads into a circular film of radius 5cm on the water surface Estimate the thickness of the film 1 8 3 x 10 10m 2 7 2 10 9m 3 8 9 10 9m 4 8 3 10 9m

Problem 3 An object of mass 0 500 kg is connected to a horizontal spring The object is pulled 25 0 cm and released from rest The object then oscillates about its equilibrium position with a period of 1 75 s a What is the spring constant of the spring b What is the object s maximum speed c Write an equation for the position as a function of time including the phase constant d What is the object s speed when it is at x 7 50 cm

completely filled with 32 A glass vessel of volume 32 liquid and its temperature is raised by AT Wh volume of the liquid will overflow Coefficient of linear expansion of glass a and coefficient of volume expansion of the liquid y a 2V AT 3 g b VAT 30 VAT d Y 3 2 29 c VAT 1 ag a Vo 1S

The bars OA and OB of lengths 4m and 6m respectively are connected to each other by one of its ends by means of a rigid element and articulated supports in A and B At point O it acts a force F We want to determine a the forces in each bar b the axial forces in each bar c the displacement of point O EOA 210 GPa B EOB 180 GPa LOB 6 m OA 4 cm 2 AOB 5 cm 2 F 40 kN F 40 kN

An air bubble at the bottom of a lake 40 0 m deep mas a volume of 1 23 cm Part A If the temperature at the bottom is 5 4 C and at the top 17 5 C what is the volume of the bubble just before it reaches the surface V A O

10 The variation of magnetic susceptibility X for a diamagnetic material with temperature is best represented by which of the following curve with respect to temperature variations 11 1 3 T 2 4 T A thin magnetic needle oscillate in the horizontal 14 1 12

A metallic wire of length and diameter 300 cm and 0 1 cm respectively is stretched by a load of 10 kg Young s modulus and Poisson s ratio for the material of the wire are 20 x 10 11 dyne cm 2 and 0 26 respectively Calculate the decrease in diameter of the wire

The water flows from a tap of diameter 1 25 cm with a rate of 5 x 10 5m s 1 The density and 3 coefficient of viscosity of water are 10 kg m 3 and 10 Pa s respectively The flow of water is 3 YOU A Steady with Reynolds number 5100 B C Turbulent with Reynolds number 5100 Steady with Reynolds number

a When two soap bubbles of different radii coalesce some portions of the surfaces make a common surface At any point on the circumference of a B and y Wha the common surface the three surfaces meet at angles relation should these angles bear a a c a y b a B Y a a B y

Four wires of the same material are stretched by 34 the same force The dimensions of wire are as given below The one which has the minimum elongation has 1 radius 3 mm length 3 m 2 radius 0 5 mm length 0 5 m 3 radius 2 mm length 2 m 4 radius 3 mm length 2 m 4 y asin cot A B C and faung fr varia i pa farart aren ant 1 fa 3 mm 3 m 2 fra 0 5 mm 3 12 mm 4 from 3 mm 2 m 0 5 m 2 m

In Searle s experiment which is used to find Young s Modulus of elasticity the diameter of experimental wire is D 0 05 cm measured by a scale of least count 0 001 cm and length is L 110 cm measured by a scale of least count 0 1 cm A weight of 50 N causes an extension of X 0 125 cm measured by a micrometer of least count 0 001cm The maximum possible error in the values of Young s modulus is x x 10 0 N m Find the value of x Screw gauge and meter scale are free from error

2 A steel wire of length 2 0 m is stretched through 20 mm The cross sectional area of the wire is 40 mm Calculate the elastic potential energy stored in the wire in the stretched condition Young modulus of steel 2 0 10 Nm2 11

12 Which of the following best describes exothermic chemical reactions They never release heat They always release heat They never occur spontaneously They always occur spontaneously 13 Which of the following represents a chemical change O water hardens into ice O wood is cut O sugar mixes with water charcoal burns

18 Two wires are made of the same material and have the same volume The first wire has cross sectional area A and the second wire has cross sectional area 3A If the length of the first wire is increased by Al on applying a force F how much force is needed to stretch the second wire by the same amount 1 4 F 2 F 3 6 F 4 9 F

Two small spherical metal balls having equa masses are made from materials of densities p and p p 8p and have radii of 1 mm and 2 mm respectively they are made to fall vertically from rest in a viscous medium whose coefficien of viscosity equals n and whose density is 0 1p The ratio of their terminal velocities would be INEET Odisha 2019 19 39 79 79

Four identical hollow cylindrical columns support a big structure of mass M The inner and outer radii of a column are R and R2 respectively Assuming the load distribution to be uniform compressional strain in each column is Y Young s modulus of column 1 3 Mg R2 R2 Y Mg T R R Y 2 4 Mg 4 R R Y Mg T R R Y

Q 95 3 2 2 One end of a metal wire is fixed to a ceiling and Q 95 a load of 2m hangs from the other end A similar wire is attached to the bottom of the load and another load of m hangs from this wire Area of cross section of each wire is same Ratio of longitudinal strain in wire 2 to that in wire 1 is wwwww 1 2 2 3 Wire 2 Wire 1 m 3 2 af en t 2m Add for a fat an organer 1 2 wwwww 2 3 Wire 2 Wire 1 m 2 21 arged 3 314 014

97 An electric fan running at a speed of 60 rpm is switched off at t 0 If the fan stops after 10 seconds the number of revolutions made by the fan till it stops is assume uniform retardation 1 10 60se 0 2 5 3 2 5 Gover Go X10 60

A uniform rod of length cross section area A and young s modulus Y is placed on a smooth horizontal surface Two horizontal forces 3F and 2F are applied at the ends of the rod as shown If the elastic potential energy stored in the rod is U n 19F 12AY Find the value of n 2F

4 One end of steel wire is fixed to ceiling of an elevator moving up with an acceleration 2 m s2 and a load of 10 kg hangs from other end Area of cross section of the wire is 2 cm The longitudinal strain in the wire is g 10 m s and Y 2 x 10 1 Nm 2 2014 a 4 10 1 b 3 x 10 6 c 8x10 6 d 2x10 6

Which of the following affects the elasticity of a substance 1 Hammering and annealing 2 Change in temperature 4 All of these d of length 2m and cross section area of 50mm stretched by 0 5mm 3 Impurity in substance