Properties of matter Questions and Answers

Example 2 6 Two clocks are being tested against a standard clock located in a national laboratory At 12 00 00 noon by the standard clock the readings of the two clocks are Monday Tuesday Wednesday Thursday Friday Saturday Sunday Clock 1 12 00 05 12 01 15 11 59 08 12 01 50 11 59 15 12 01 30 12 01 19 Clock 2 10 15 06 10 14 59 10 15 18 10 15 07 10 14 53 10 15 24 10 15 11 If you are doing an experiment that requires precision time interval measurements which of the two clocks will you prefer

The mean pressure is 6K 5 which rain renders to vertical windshield of automobile moving with constant velocity of magnitude v 12 m s Consider that raindrops fall vertically with speed u 5 m s The intensity of rainfall deposits h 2 cm of sediments in time t 1 minute p 10 kg m is the density of liquid Assume collisions are inelastic

8 A thick rope of rubber of length 8 m and density 1 5 10 kg m has Young s modulus 3 5x 106 Nm 2 When hung from ceiling of a room the increase in length due to its own weight is a 96 10 3 m b 19 2x 10 5 m c 9 4 cm d 9 6 mm

22 Aballoon of volumie V contains a gas of mass mat a pressure P and temperature 15 C Gas is pumped into the balloon so that its volume is doubled and the pressure is trebled If the temperature increases 6 C in the process finc the ratio of the increase in mass to the origi nal mass 1 34 5 2 239 49

Two equal and opposite forces each of magnit F is applied along a rod of transverse sectional area A The normal stress to a section PQ inclined to transverse section is ar 0 F 1 3 F sine A sin 20 2 4 P F A A Q AS cose Ecos 0 F

In a Quincke s tube there are two positions where sound becomes minimum the sliding distance between the is 16 6 cm Find the freq of sound source Sound velocity in air 332 m sec A tuning fork having frequency 300 Hz produce four beats ner ser with x If we file arm of unknown and ag

13 Volume of a substance at normal atmospheric pressure is 3500 10 6 m What will be its change in volume at the pressure of 25 standard atmosphere Given that bulk modulus of the substance is 1011 N m 2 85 x 10 9 m

stration 5 2 Assume that if the shear stress in steel exceeds about 4 00 x 108 N m the steel reptures Determine the shearing force necessary to a shear a steel bolt 1 00 cm in diameter and b punch a 1 00 cm diameter hole in a steel plate 0 500 cm thick

A pipe of circular cross section of inner radius r and outer radius 2r is bent into a semi circle as shown in the diagram A fluid of density p 10 kg m is flowing through it The breaking stress of the material of the pipe is 3 x 10 N m The maximum velocity with which the fluid can flow in the pipe is kx 100 m s Find value of k 9

34 Density of ice is p and that of water is o What will be decrease in volume when a mass M of ice melts 1 M o p 1 3 M 2 4 o p M M 10

11 The increase in pressure required to decrease the 200 L volume of a liquid by 0 008 in kPa is Bulk modulus of the liquid 2100 MPa is 1 8 4 2 84 3 92 4 4 168

30 Two steel rods and an aluminium rod of equal length l and equal cross section are joined rigidly at their ends as shown in the figure below All the rods are in a state of zero tension at 0 C Find the length of the system when the temperature is raised to 0 Coefficient of linear expansion of aluminium and steel area and a respectively Young s modulus of aluminium is Y and of steel is Y Steel 1390 Aluminium Steel O

13 A steel rod is 4 cm in diameter at 30 C A brass ring has an interior diameter of 3 992 cm at 30 C In order that the ring just slides on to the steel rod the common temperature of the two rods should be a 11x10 6 1 C a 19x10 6 1 C 1 200 C 2 350 C 3 280 C 4 300 C

25 If S is stress and Y is young s modulus of material of a wire the energy stored in the wire per unit volume is a S 2Y b 2S Y c S 2Y d 2Y S

Two objects A B of equal density and radius TA 1 mm and r 2 mm are moving in same medium then find the ratio of their terminal velocity VB B in the medium 2 1 2 VA 1 1 4 43 4 4 2

The diagram shows a simple mercury barometer The mercury level is at a heighth when the atmospherich P pressure is 100000 Pa What is the pressure at P A 40000 Pa B 60000 Pa C 100000 Pa D 140000 Pa 0 4 h

A wire elongates by mm when a load W is hanged from it If the wire goes over a pulley and two weights W each are hung at the two ends the elongation of the wire will be in mm 4 zero 1 l 2 2 l 3 2 Y in mode of a material of density o It is falling through a liquid of density p p AIEEE 2006

4 length 50 cm diameter 0 5 mm 3 length 300 cm diameter 3 mm Copper of fixed volume V is drawn into wire of length e When this wire is subjected to a constant force F extension produced in the wire is Al Which of the following graph is a straight line 4 Al versus l AIPMT 201 1 Al versus 1 2 Al versus l 3 Al versus 1 1

4 Length 300 cm Diameter 3 mm 3 Length 200 cm Diameter 2mm A catapult s string made of rubber having cross section area 25 mm and length 10 cm To throw a 5 gm pabble it is stret up to 5 cm and released Velocity of projected pabble is Young coefficient of elasticity of rubber is 5 108 N m 1 20 m s 2 100 m s 3 250 m s RPMT 25 4 200 m s 9 x 101 N m Force required to increa

A 5m aluminium wire Y 7 x 1010 N m of diameter 3 mm supports a 40 kg mass In order to have the sam elongation in a copper wire Y 12 x 10 0 N m of the same length under the same weight the diameter should be RPMT 2007 mm 1 1 75 2 2 0 3 2 3 4 5 0

4 One end of a uniform wire of length L and of Wo is attached rigidly to a point in the roof and a weight W is suspended from its lower end If S is the area of cross section of the wire the stress in the wire at a height L 4 from its lower end is 1 W S 2 W 2 W W 4 S 3 W 3W 4 S 4 W W S

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of 0 1 gm sec It melts completely in 100 sec The rate of rise of temperature thereafter will be Assume no loss of heat 0 8 C sec 2 5 4 C sec 3 3 6 C sec 4 will change with time 1

3 450 MJ m 25 A uniform wire of length 3m and mass 10 kg is suspended vertically from one end and loaded at other end by a block of mass 10 kg The radius of cross section of wire is 0 1 m The stress in the middle of wire is g 10 m s 1 1 4 x 104 N m 2 4 8 x 103 N m 3 96 104 N m 4 35 10 N m

A steel wire of length 4 2 m and cross sectional area 3 x 10 5 m stretches by the same amount as a copper wire of length 3 5 m and cross sectional area 4 105 m under given load What is ratio of Young s modulus of steel to that of copper 05 8

4 viscosity A certain number of spherical drops of a liquid of radius r coalesce to form a single drop of radius R and volume V If T is the surface tension of the liquid then AIPMT 2014 1 Energy 4VT 1 3 Energy 3VT R is released is released 2 Energy 3VT is released 4 Energy is neither released nor absorbed of capillary tube above the surface of water is made less than

A soap bubble of diameter 8 mm is formed in air The surface tension of liquid is 30 dyne cm The excess pressu inside the soap bubble is 1 150 dyne cm 2 300 dyne cm 3 3 x 10 3 dyne cm 4 12 dyne cm

17 Water is filled up to a height h in a beaker of radius R as shown in the figure The density of water is p tension of water is T and the atmospheric pressure is P Consider a vertical section ABCD of the water column through a diameter of the beaker The force on water on one side of this section by water on the other side of this section has magnitude 1 2P Rh nR pgh 2RT 3 PR R pgh 2RT 2R A B 2 2P Rh Rpgh 2RT 4 PR R pgh 2RT

A capillary tube of radius R is immeresed in water and water rises in it to a height H Mass of water in capillary tube is M if the radius of the tube is doubled mass of water that will rise in capillary tube will be 1 2M 2 M 3 M 4 4M 2 bubble of radius r r The radius R of the soapy film

The lengths and radii of two rods made of same material are in the ratios 1 2 and 2 3 respectively If the temperatu difference between the ends for the two rods be the same then in the steady state the amount of heat flowing per seco through them will be in the ratio 1 1 3 2 4 3 3 8 9 4 3 2

A partition divides a container having insulated walls into two compartments I and II The same gas fills the two compartments see Fig The ratio of the number of molecules in compartments I and II is ya fue dart ist m area fearger ergen at CI P V T ima a A 1 6 B 6 1 C 4 1 D 1 4 2P 2V T

Water rises in a capillary tube of radius r upto a height h The mass of water in a capillary r of radius will be 4 m The mass of water that will rise in a A m B 4m C m enc capilar m aque

9 What kind of elastic materials are derived from a strain energy density function a Cauchy elastic materials b Hypo elastic materials c Hyper elastic materials d None of the mentioned I

8 As the elastic limit reaches tensile strain a Increases more rapidly b Decreases more rapidly c Increases in proportion to the stress d Decreases in proportion to the stress

A gas undergoes a process in which its pressure P and volume V are related as VP constant The bulk modulus the gas in the process is 1 nP 2 p n 3 P n 4 Pn

Q1 The pressure at a depth of 700 m in the ocean is around 7 kPa By how much does the volume of 0 2 m aluminum cube contract when it is dropped this depth of the ocean O A 0 2 m O 8 Aluminum cube will not contract O c 20 mm O D 0 2 mm

When a spring is subjected to 4N force its length is a metre and if 5N is applied length is b metre If 9N is applied its length is A 4b3a C 5b 4a B 5b a D 5b 2a 135

72 Two soap bubbles of the same soap solution have radii 3 cm and 1 5 cm If the excess pressure inside the bigger bubble is 40 dyn cm what is the excess pressure inside the smaller bubble 1 mark

The temperature gradient in a rod of 0 5 m length is 80 C m If the temperature of hotter end of the rod is 30 C then the temperature of the cooler end is Question Type Single Correct Type 1 40 C 2 10 C 3 10 C

Ques 4 A pipe 10 cm in diameter contains steam at 100 C It is covered with an insulating material that is 5 cm thick This insulating material has a constant of thermal conductivity K 0 0006 The outside surface of the system is 30 C Find the heat loss per hour from a meter length of the pipe

9 Two similar rods of length 1 and I each of iron and b respectivel expansion of iron and brass are a and raised then determine the relation 1 1 A Oa a a B Oa a a C Oa a ap D O aa

A glass capillary tube is of the shape of truncated cone with an apex angle a so that its two ends have cross sections of different radii When dipped in water vertically water rises in it to a height h where the radius of its cross section is b If the surface tension of water is S its density isp and its contact angle with glass is the value of h will be g is the acceleration due to gravity 2014 Adv

1 Rises 2 Falls 3 A large ship can float but a steel needle sinks because of 1 Viscostiy 2 Surface tension 3 Density The Working of an atomizer depends upon 4 None of these

3 A steel ring of radius r and cross sectional area A is fitted on to a wooden disc of radius R R r It Young s modulus of steel is Y then stress in the steel ring is 1 3 RY r 2 4 R ry r F y

A steel wire of length 2 m is stretched through 2 mm What is elastic potential energy stored in a wire of cross sectional area 4 mm in stretched condition Y 2 x 10 1 Nm 0 8 J O 1 2 J 2 4 J 1 6 J

4 atoms contains negatively charged particles 32 Graph of total number of a particles scattered at different angles is Number of a particles Number of 14 20 160 0 20 160 0 a particles 4 32 fafan 19 Lin 40 70 Ita F 14 10 42 70 2 F341 20 160 0 20 160 0 E

why is the Reynolds number taken as 2000 while as per ERT the laminar or steady flow is less than 1000 plit increases Discuss qualitatively 10 26 a What is the largest average velocity of blood flow in an artery of radius 2x10 m if the flow must remain lanimar b What is the corresponding flow rate Take viscosity of blood to be 2 084 x 10 3 Pa s

4 0 12 15 Two exactly similar wires of steel and copper are stretched by equal forces If the total elongation is 2 cm then how much is the elongation in steel and copper wire respectively Given Y 20 1011 dyne cm2 Ycopper 12 x 10 1 dyne cm 1 1 25 cm 0 75 cm 2 0 75 cm 1 25 cm 3 1 15 cm 0 85 cm 4 085 cm 115 cm

The excess pressure inside an air bubble of radius r just below the surface of the water is P The pressure inside a drop of the same radius just outside the surface is P2 If T is the surface tension then AP 2P Your Answer B P P Correct Answer P 2P DP 0 P 0

Problem 249 A vertical cylinder of radius R is rotating with a constant angular velocity o along with holders A and B about the axis as shown The vertical movement of cylinder is restricted by the holders Oil is only in between the bottom of cylinder and surface as shown The thickness of the oil layer is t Assume that coefficient of viscosity is n and that cylinder can only rotate if there is no friction elsewhere Find the power required to overcome the viscous resistance A R

38 A wire fixed at the upper end stretches by length by applying a force F The work done in stretching is AIEEE 2004 a F 21 b Fl FI