Properties of matter Questions and Answers

Aliquid enter at point A1 with speed 3 5 m s and leaves at point A2 Then find out the height attained by the liquid above point A2 A V 1 61 25 cm 3 41 25 cm A V AIIMS 2019 2 51 25 cm 4 71 25 cm

A steel rod of 30 mm diameter is enclosed centrally in a hollow copper tube of external diameter 50 mm and an internal diameter of 40 mm shown in Figure 2 This composite bar is then subjected to an axial pull of 50 000N If the length of each bar is equal to 200 mm determine The stresses in the rod and tube Load carried by each bar i ii 200 P 50 000N All dimensions are in mm Copper Tube Steel Rod

A square steel rod 20 mm x 20 mm in section is to carry an axial load compressive of 100 kN Calculate the shortening in a length of 50 mm E 2 14 108 kN m 0 0854 mm 0 0684 mm 0 0784 mm 0 0584 mm

A metal rod is placed on smooth horizontal surface at temperature 25 C Now temperature of surroundings is increased up to 100 C then during heating of rod 1 Mechanical strain developed in rod is nonzero 2 Mechanical stress developed in rod is nonzero 3 Length of rod will increase 4 All of these

A wire of length 2 5 m is attached with a load of 3 kg The change in length observed is 0 1 and stress is 170 45 kg cm 2 hence Young s modulus of material of wire is N m 2 CO2 O 1 7 x 10 10 O 1 67 x 10 10 O 1 7 x 10 9 167 x 10 11

62 Hydrogen atom in ground state is excited by a monochromatic radiation of 975 Number of spectral lines in the resulting spectrum emitted will be 2014 a 3 a b 2 d 10

The approximate depth of an ocean is 2700m The compressibility of water is 45 4 x 10 Pa and density of water is 10 kg m What fractional compression of water will be obtained at the bottom of the ocean

A stress strain diagram is shown for a hypothetical tensile test specimen of a hypothetic material Dotted line shows the unloading curve and the dark line shows the loading cur of the specimen The values of the Young s modulus and the permanent set at the im cated position are Stress MPa 150 50 0 0 10 05 a 1000 MPa and 0 10 c 100 GPa and 0 10 0 25 Permanent set 0 40 Strain b 100 GPa and 0 15 d None of the above

98 A slender prismatic rod is fixed between the two non yielding supports as shown in the figure below The temperature of the rod is now raised by 100 C Assume area of the rod to be 1000 mm Young s modulus of elasticity of the rod material as 200 GPa and coefficient of thermal expansion of the rod to be 1 x 10 6 C The stress developed in the rod because of the temperature change will be b 15 MPa a 20 MPa c 5 MPa 100 mm 0 005 mm d 10 MPa its mid point Which of the following will

7 The stress strain behaviour of a material is shown in the following figure Its resilience and toughness in Nm and m Stress MPa respectively are a 28 104 76 104 b 28 x 104 48 104 c 14 104 90 104 d 76 104 104 104 120 90 70 60 30 0 004 0 008 0 012 Strain mm mm

To break a wire a force of 106 N m is required If the density of the material is 3 x 10 kg m then the length of the wire which will break by its own weight will be 1 34 m 2 30 m 3 300 m 4 3 m

Q From the ceiling a light rod of length 200 cm is suspended horizontally with the help of two vetical wires of equal lenght as shown in figure If one wire is made of brass and have cross sectional area 0 2 cm and other of steel of 0 1 cm of cross sectional area then at what distance along rod a weight may be hung to produce equal stress in both the wires Steel wire 200 cm Brass wire

A capillary tube of radius r is lowered into water whose surface tension is a and density d The liquid rises to a height Assume that the contact angle is zero Choose the correct statement s Magnitude of work done by force of surface tension is 470 dg Magnitude of work done by force of surface tension is 2700 dg Potential energy acquired by the water is The amount of heat developed is 2 700 da 270 dg

A cube is subjected to pressure of 5 x 105 Nm 2 Each side of the cube is shortened by 1 Find volumetric strain and bulk modulus of elasticity of cube 2 2 a 0 5 4 2 x 105 N m2 b 0 03 1 67 x 107 Nm c 1 2 2 5 x 105 N m2 d 0 3 2 2 x 10 N m 2

0 A wire hangs vertically under its own weight The specific weight of wire is 100 n m and maximum permissible tensile stress is 100 n mm2 The greatest length that can be hung is b 100m d 10 000m a 10m c 1000m

Two metal rods A and B of uniform cross section and identical dimensions is held fixed between two immobile rigid supports on both sides The coefficient of linear thermal expansion of the rod B is twice that of the rod A If the temperature of the rods is increased uniformly by 2 C and if the stress developed in the rod B is one half of the stress developed in the rod A then A Y 2 Y 8 Y 8Y 0 Y 4Y nY 282 Y

c 55 A circuit area 0 01 m is kept inside a magnetic field which is normal to its plane The magnetic field changes from 2 tesla to 1 tesla in 1 millisecond If the resistance of the circuit is 2 2 The rate of heat evolved is a 51 s c 0 05 l s b 50 l s d 0 5J s

Q No 11 A cable that can support a load W is cut into two equal parts The maximum load that can be supported by either part is 2 3 Correct Answer 3 Your Answer 2 Status incorrect WWLWW 4 2 2W Vi

If the ratio of lengths radii and Young s modulii of stee and brass wires in the figure are a b c respectively The the corresponding ratio of increase in their length would be 1 2 3 2ae 2m 3a 26 m 3c 2ab Steel Brass

c 11 8 x 10 Am d 1 18 x 10 Am 4 A magnetising field of 2 x 10 A m produces a magnetic flux density of 8 x T in an iron rod The relative permeability of the rod will be a 10 b 1 c 10 d 10

A solid sphere of radius R made of material of bulk modulus k is surrounded by a liquid in a cylindrical container A massless piston of area A floats on the surface of the liquid When a mass M is placed on piston to compress the liquid The liquid in turn puts a pressure on the sphere The fractional change in the surface area of sphere due to mass M is Mg B 3AK Mg AK 3AK 5Mg C D 2Mg 3AK

Q1 A glass capillary tube is of the shape of a trun cated 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 is p and its contact angle with glass is the value of h will be where g is acceleration due to gravity 2014 2 S bpg A cos a B cos 8 2 2S cos 0 a cos 8 a 2

1 0 km deep in sea Density of sea 1 025 x 10 kg m Bulk modulus of object 1 6 106 KPa Find out percentage change in density of obje 1 0 36 2 0 64 3 0 40 4 0 60

A water drop of radius 1 5 mm is falling from height 1 km having drag constant 0 5 density of water drop is 1000 kg m and density of air is 1 29 kg m Find its terminal velocity 1 8 7 m s 3 5 6 m s 2 7 8 m s 4 4 3 m s

In a double slit experiment the wavelength of monochromatic light used is and the separation between the slits is d The screen is located at a distance D from the slits If a bright fringe is formed on the screen directly opposite to one of the slits the order of the fringe is d 2D A B C D d 2 D d D D d

The young s modulus E of a material measures how stiff it is the larger value of the morete tiff the material Consider a solid rectangular steel beam which is anchored horizontally to he wall at one end and allowed to deflect under its own weight The beam has length L wertical thickness h width w mass density p and Young s modulus E the acceleration due to gravity is g What is the distance through which the other end moves Hint you are expected o solve this problem by eliminating implausible answers Also note that all the options are Himensionally correct pgh a 2 b 2Lh 3 pg 4 2 r1 2 d 3 EL ngh

A body of mass 0 01 kg starts to move in a viscous liquid with initial velocity 5 m s If drag force is 10 3 N then find time after which velocity will become 1 10 1 49 sec 3 149 sec m s 2 100 sec 4 200 sec P 33m

Assume that if the shear stress in steel exceeds about 4 00 108 N m the steel ruptures a Determine the shearing force necessary to shear a steel bolt 1 35 cm in diameter b Determine the shearing force necessary to punch a 1 35 cm diameter hole in a steel plate 0 940 cm thick

The shear modulus of lead is 2 x 10 Pa A cubic lead slab of side 50 cm is subjected to a shearing force of magnitude 9 0 x 10 N on its narrow face see figure The displacement of the upper edge is AC where A is A 2 x 10 m B 5 x 10 m 50 cm C 4 x 10 m Al Bottem is riveted to the floor D 9 x 105 m

The Poisson s ratio of a material is 0 2 Due to a certain force length of wire elongates by 0 1 The percentage change in the volume of wire will be 0 6 0 2 0 3 0 14

Following four wires are made of same material Which will have maximum extension when subjected to same tension Length 10 cm radius 1 mm Length 20 cm radius 0 5 mm Length 5 cm radius 2 mm Length 30 cm radius 2 mm

Liquid rises in a capillary upto a height of 8 cm The internal and external diameters of a second capillary are double that of first capillary the height of liquid in it will be Question Type Single Correct Type 1 2 8 cm 4 4 cm 3 2 cm 1 cm

A block of mass 8 kg is placed on a surface as shown The dimensions of the box is 40cm x 20 cm x 10 cm What is the pressure applied by it Assume g 10 m s 20 cm How would the pressure change if the block is placed on the longer side as shown

17 The proportional limit of steel is 8 x 108 N m2 and its Young s modulus is 2 x 10 11 N m2 The maximum elongation a one metre long steel wire can be given without exceeding the elastic limit is 1 2 mm 2 4 mm 3 1 mm 4 8 mm

To protect a sensitive instrument from external megnetic jerks it should be placed in a container made of 1 Non magnetic substance 2 Diamagnetic substance 3 Paramagnetic substance 20

A steel bar 1 25 cm in diameter and 5 cm long is removed from a 1200 C furnace and placed in a container of water at atmospheric pressure Estimate the heat transfer rate from the bar when it is first placed in the water

Match the following A D converters with thei properties Types of A D converters A Dual Slope B Counter ramp C Successive Approximation Properties of A D converters 1 Fixed conversion time depends on the no of bits 2 High speed operation 3 Hum rejection 4 Conversion time D Simultaneous dependent on signal

1 A rigid bar of weight W 900 KN is kept horizontal by the two rods one of aluminium and the other of steel Fig 3 93 Find the ratio of the areas of the rods so that the bar remains horizontal E 70 GPa for aluminium and 200 GPa for steel

A capillary of radius r 0 2 mm is dipped vertically in a liquid of density p 1 gm cc A small piston x is inserted inside the capillary which maintains constant the pressure of air above hemispherical meniscus P 5 dynes m If atmospheric pressure Po 10 dynes cm and surface tension of liquid T 72 dynes cm then find the height h of liquid g 1000 cm s weight of curved part of liquid is ignored write your answer in cm upto 4 decimal place

An oil drop of 10 excess electrons is held stationary under a constant electric field of 3 65 x 10 NC in Millikan s oil drop experiment The density of oil is 1 26 g cm Radius of the oil drop is Take g 9 8 ms2 e 1 6 x 10 19 C a 1 04 x 10 6 m c 4 8 x 10 18 m b 4 8 x 10 5 m d 1 13 x 10 18 m

P A certain current liberates 0 504 g of hydrogen in 2 hr How many gram of copper can be liberated by the same current flowing for the same time in CuSO4 solution a 12 7 c 31 8 b 16 d 63 5 inn faraday of charge through aqueou

SolveLancer Test Consider the diagram where block has weight of 200N AB and CD are two wires of different mater having same cross sectional area Due to block the elongation in wire AB is ALAB and in wire CD is Alco then value of 45 2m ND 200 N 30 2m Given Young s modulus for both wires is YcD 2YAB SolveLancer Test a 2 3 2 b 1 2 3 c 3 3 2 d 1 3 3

45 One mole of gas of specific heat ratio 1 5 being initially at temperature 290 K is adiabatically compressed to increase its pressure 8 times The of the gas after compression will be temperature a 580 K c 290 2 K b 870 K d 1160 K

An iron bar Young s modulus 1011 N m a 10 6 C 1 m long and 10 3 m in area is heated from 0 C to 100 C without being allowed to bend or expand Find the compressive force developed inside the bar O 10 000 N O 1000 N 5000 N O 105 N r

3 Stress A Strain Stress B Strain Choose the correct statement 1 Material in A is ideal to make thin wire Material in B is ideal to make thin wire 3 Both materials in A and B are ideal to mak thin wire 4 Both materials in A and B are not good make thin wire

A uniform metal rod of 2mm2 cross section is heated from 0 C to 20 C The coefficient of linear expansion of rod is 12 x 10 6 C Its young s modulus of elasticity is 1011 N m2 The energy stored per unit volume of rod if the rod is free to expand is 1 zero 3 5760 J m 2 1500 J m 4 1440 J m

29 Calculate the thermal stress developed in a rod kept on a smooth surface as shown in figure if the temperature of rod is increased by AT Y young s modulus acoefficient of thermal expansion A cross section area 1 y a AT 3 Zero Rod smooth horizontal 2 a AT 4 YA AT

9 A hole is drilled in a copper sheet The diameter of the hole is 4 24 cm at 27 0 C What is the change the diameter of the hole when the sheet is heated to 227 C Coefficient of linear expansion of copper is 1 70 x 10 5 C 1 a 1 44 x 102 cm 2 44 x 103 cm c 1 44 x 10 2 mm d 2 44 x 10 mm b

c A ball of mass m and radius r is released in 7 The viscous liquid The value of its terminal velocity is and proportional to 481 a 1 r only c m r 2 a b mir d monly l contains a mixture consisting of m 7 g of 8 W a

A brass rod of cross sectional area 1 cm and length 0 2 m is compressed lengthwise by a weight of 5 kg If Young s modulus of elasticity of brass is 1 x 10 1 N m and g 10 m s then increase in th energy of the rod will be O 10 5 J 02 5 x 10 5 J 0 5x10 5 J 02 5 x 10 4 J