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Mechanical Properties of Solids — JEE Main & Advanced Physics PYQs

249 previous year questions from Mechanical Properties of Solids with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

249 questionsPhysicsSolutions on every page
1

Figure represents the extension ( l ) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load W connected to the other end. If the cross-sectiona

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2

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 10^8 N/m ^2 and its radius is 4 mm, then maximum acceleration the li

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3

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11 . When the joined wire is ke

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4

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600 10⁻⁶ m ^3 . The elastic potential energy stored in the wire in stretch

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5

The Young's modulus of steel wire of radius r and length L is Y . If the radius r and length L of the wire are doubled then the value of Y

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6

Two wires as shown in the figure below, made of steel and have breaking stress of 12 10^8 N/m ^2 . Area of cross-section of upper wire is 0.008 cm ^2 and of lower wire is 0.004 cm

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7

A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement produced by a force of 10 N in the upper face of cube is _____ mm.

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8

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M . Second block having mass 2M is suspended at the bottom of the first block usi

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9

The increase in the pressure required to decrease the volume ( V) of water is 6.3 10^7 N/m ^2 . The percentage decrease in the volume is _____. (Bulk modulus of water = 2.1 10^9 N/

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10

A string A of length 0.314 m and Young's modulus 2 10¹⁰ N/m ^2 is connected to another string B of length and Young's modulus both twice of those of A . This series combination of

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11

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is appli

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12

A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l 3 distance from the top is ( W A + 2 w A ) , wher

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13

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 10⁻⁵ ~m ² and 4.5 10⁻⁵ ~m ² , respectively are stretched by

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14

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus ?

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15

A 3 m long wire of radius 3 mm shows an extension of 0.1 mm when loaded vertically by a mass of 50 kg in an experiment to determine Young's modulus. The value of Young's modulus of

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16

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 ~cm ^3 . If the bulk modulus of the liquid is 2 GPa , the initial volume of

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17

Two wires A and B are made of same material having ratio of lengths L_A L_B = 1 3 and their diameters ratio d_A d_B =2 . If both the wires are stretched using same force, what woul

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18

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 10^5 ~N at the top. Considering infinitesimally small displacement in the

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19

Two slabs with square cross section of different materials (1,2) with equal sides (l) and thickness d ₁ and d ₂ such that d ₂=2 ~d ₁ and l d ₂ . Considering lower edges of these sl

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20

A steel wire of length 2 m and Young's modulus 2.0 10¹¹ Nm ⁻² is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 10⁻³ respectively, then the e

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21

The fractional compression ( ( V V ) ) of water at the depth of 2.5 km below the sea level is ______ ( % ). Given, the Bulk modulus of water (=2 10^9 ~N ~m ⁻² ), density of water (

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22

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7 10^6 ~Pa , would be ____ mm ^3 . (Given bulk modulus of copper =1.4

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23

The increase in pressure required to decrease the volume of a water sample by 0.2 % is P 10^5 Nm ⁻² . Bulk modulus of water is 2.15 10^9 Nm ⁻² . The value of P is

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24

Two persons pull a wire towards themselves. Each person exerts a force of 200 ~N on the wire. Young's modulus of the material of wire is 1 10¹¹ ~N ~m ⁻² . Original length of the wi

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25

A wire of cross sectional area A, modulus of elasticity 2 10¹¹ Nm ⁻² and length 2 ~m is stretched between two vertical rigid supports. When a mass of 2 ~kg is suspended at the midd

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26

Match List-I with List-II : array |c|c|c|c| & List-I & & List-II (A) & A force that restores an elastic body of unit area to its original state & (I) & Bulk modulus (B) & Two equal

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27

The density and breaking stress of a wire are 6 10^4 ~kg / m ^3 and 1.2 10^8 ~N / m ^2 respectively. The wire is suspended from a rigid support on a planet where acceleration due t

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28

An elastic spring under tension of 3 ~N has a length a . Its length is b under tension 2 ~N . For its length (3 a-2 b) , the value of tension will be______ N .

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29

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from

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30

With rise in temperature, the Young's modulus of elasticity

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31

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is 4 . 0 × 10 - 5 m and Young's modulus of the meta

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32

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by 0 . 02 % is _____ m . (Take density of sea water = 10 3 kg m - 3 , Bulk modulus o

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33

Young's modules of material of a wire of length L and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's modules wil

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34

Each of three blocks P , Q and R shown in figure has a mass of 3 kg . Each of the wire A and B has cross-sectional area 0 . 005 cm 2 and Young's modulus 2 × 10 11 N m - 2 . Neglect

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35

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F , its length increases by l . If the radius of the wire and the applied force both ar

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36

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force F 1 is applied to P , an extension of

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37

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A) : The property of body, by virtue of which it tends to regai

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38

If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 10 9 N m - 2 , then fractional compression Δ V V of water at the bottom of ocean is α × 10 - 2 . The val

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39

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f , its length increases by l . Another wire of same material of

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40

Under isothermal condition, the pressure of a gas is given by P = a V – 3 , where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is

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41

The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J . The cross sectional area of the wire is _____ mm 2 . (Given, Y = 2 . 0 × 10

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42

The length of a wire becomes l 1 and l 2 when 100 N and 120 N tension are applied respectively. If 10 l 2 = 11 l 1 , then the natural length of wire will be 1 x l 1 . Here the valu

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43

Young’s moduli of the material of wires A and B are in the ratio of 1 : 4 , while its area of cross sections are in the ratio of 1 : 3 . If the same amount of load is applied

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44

Two wires each of radius 0 . 2   cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is _

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45

An aluminium rod with Young’s modulus Y = 7 . 0 × 10 10 N m - 2 undergoes elastic strain of 0 . 04 % . The energy per unit volume stored in the rod in SI unit

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46

A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm . The tensile stress developed in the wire under equilibrium state is 7 × 10 5

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47

A steel rod has a radius of 20   mm and a length of 2 . 0   m . A force of 62 . 8   kN stretches it along its length. Young's modulus of steel is 2 . 0 × 10

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48

The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm 2 , is 2 × 11 11 N / m 2 . The wire is suspended from its support on a given planet. A bloc

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49

A certain pressure ' P ' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0 . 01 % whereas the liquid gets compressed to 0 . 03 %

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50

Under the same load, wire A having length 5 . 0 m and cross section 2 . 5 × 10 - 5 m 2 stretches uniformly by the same amount as another wire B of length 6 . 0 m and a cross s

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51

A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0 . 2 mm . If same force is applied to another steel wire B of double the l

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52

Choose the correct relationship between Poisson ratio σ , bulk modulus ( K ) and modulus of rigidity η of a given solid object:

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53

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin an

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54

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion (A) : Steel is used in the construction of buildings and bridges. Rea

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55

A 100 m long wire having cross-sectional area 6 . 25 × 10 - 4 m 2 and Young's modulus is 10 10 N m - 2 is subjected to a load of 250 N , then the elongation in the wire wi

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56

A metal wire of length 0 . 5 m and cross-sectional area 10 - 4 m 2 has breaking stress 5 × 10 8 N m - 2 . A block of 10 kg is attached at one end of the string and is rotating

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57

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will :

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58

A string of area of cross-section 4 mm 2 and length 0 . 5 is connected with a rigid body of mass 2 kg . The body is rotated in a vertical circular path of radius 0 . 5 m . The body

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59

The force required to stretch a wire of cross-section 1 cm 2 to double its length will be : (Given Yong's modulus of the wire = 2 × 10 11 N m - 2 )

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60

A steel wire of length 3 . 2 m Y S = 2 . 0 × 10 11 N m - 2 and a copper wire of length 4 . 4 m Y C = 1 . 1 × 10 11 N m - 2 , both of radius 1 . 4 mm are connected end to

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61

In an experiment to determine the Young's modulus, steel wires of five different lengths ( 1 , 2 , 3 , 4 and 5 ) but of same cross-section 2   mm 2 were taken and curves b

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62

A square aluminium (shear modulus is 25 × 10 9 Nm - 2 ) slab of side 60   cm and thickness 15   cm is subjected to a shearing force (on its narrow face) of 18 . 0 &#

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63

The area of cross section of the rope used to lift a load by a crane is 2 . 5 × 10 - 4 m 2 . The maximum lifting capacity of the crane is 10 metric tons. To increase the lifti

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64

A uniform heavy rod of mass 20 kg . Cross sectional area 0 . 4 m 2 and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod du

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65

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F , its length increases by 5 cm . Another wire of the same mater

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66

A wire of length L is hanging from a fixed support. The length changes to L 1 and L 2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is

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67

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 × 10 - 4 is _____ kJ m - 3 . Assume

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68

The bulk modulus of a liquid is 3 × 10 10 Nm - 2 . The pressure required to reduce the volume of liquid by 2 % is :

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69

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 10 3 kg . The inner and outer radii of each column are 50 cm and 100 cm respective

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70

A uniform heavy rod of weight 10 kg m s - 2 , cross-sectional area 100 cm 2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 × 1

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71

When a rubber ball is taken to a depth of _______ m in deep sea, its volume decreases by 0 . 5 % (The bulk modulus of rubber = 9 . 8 × 10 8 N m - 2 Density of sea water = 10 3

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72

Wires W 1 and W 2 are made of same material having the breaking stress of 1 . 25 × 10 9 N m - 2 . W 1 and W 2 have cross-sectional area of 8 × 10 - 7 m 2 and 4 × 10

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73

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24 π × 10 2 N m - 2 . What is the minimum

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74

A stone of mass 20   g is projected from a rubber catapult of length 0 . 1   m and area of cross section 10 - 6   m 2 stretched by an amount 0 . 04   m . The ve

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75

Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y 1 and Y 2 . The combination behaves as a single

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76

The area of cross-section of a railway track is 0 . 01   m 2 . The temperature variation is 10   ° C . Coefficient of linear expansion of material of track is 10 - 5

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77

The length of a metal wire is ℓ 1 , when the tension in it is T 1 and is ℓ 2 when the tension is T 2 . The natural length of the wire is:

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78

The value of tension in a long thin metal wire has been changed from T 1 to T 2 . The lengths of the metal wire at two different values of tension T 1 and T 2 are ℓ 1 and &#8

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79

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N . Assume that both the wires are made up of same material and the

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80

An object is located at 2 km beneath the surface of the water. If the fractional compression Δ V V is 1 . 36 % , the ratio of hydraulic stress to the corresponding hydraulic s

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81

The length of metallic wire is l 1 when tension in it is T 1 . It is l 2 when the tension is T 2 . The original length of the wire will be :

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82

The normal density of a material is ρ and its bulk modulus of elasticity is K . The magnitude of increase in density of material, when a pressure P is applied uniformly on all

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83

A uniform metallic wire is elongated by 0 . 04 m when subjected to a linear force F . The elongation, if its length and diameter is doubled and subjected to the same force will be

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84

If Y , K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

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85

A cubical solid aluminum bulk modulus = - V d P d V = 70 GPa block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the a

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86

A cube of metal is subjected to a hydrostatic pressure 4 G P a . The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 &#215

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87

A wire of density 9 × 10 – 3 kg cm – 3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4 . 9 × 10 – 4 . The lowest freque

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88

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4 , the ratio of their diameters is:

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89

A body of mass m = 10   k g is attached to one end of a wire of length 0.3   m . What is the maximum angular speed (in r a d   s - 1 ) with which it can be rotated a

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90

Speed of a transverse wave on a straight wire (mass 6.0 g , length 60 c m and area of cross-section 1.0 m m 2 is 90 m s - 1 . If the Young's modulus of wire is 16 × 10 11

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91

Two metal strips are riveted together at their ends by four rivets, each of diameter 6   mm . Assuming that each of the rivets carries one-quarter of the load, the maximum te

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92

A solid sphere made out of metal having a bulk modulus of 2 × 10 11 Nm - 2 is charged uniformly to a surface charge density σ = α ε 0 Cm - 2 , where ε 0 is the permittivity of free

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93

A cube of aluminium of side 6   cm is subjected to a tangential force such that the top face is shears through 0.012   cm relative to the bottom face. The tangential forc

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94

A stone of mass 1 . 3   kg is being rotated in a horizontal plane as a conical pendulum with the help of a 140   cm long aluminium wire of cross-sectional area 1   m

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95

A uniform rod of length l is acted upon by a force F in a gravity-free region, as shown in the figure. If the area of cross-section of the rod is A and it's Young's modulus is Y ,

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96

A particular force F applied on a wire increases its length by 2 × 10 - 3 m . If we were to increase the wire's length by 4 × 10 - 3 m , then the applied force is n F . What is the

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97

One of the square faces of a metal slab of side 50   cm and thickness 20   cm is rigidly fixed on a horizontal surface. If a tangential force of 30   N is applied to

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98

Two wires of the same material (Young's modulus Y ) and same length L but radii R and 2 R respectively are joined end to end and a weight w is suspended from the combination as sho

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99

A thin rod of negligible mass and area of cross-section 4 × 10 - 6 m 2 , suspended vertically from one end, has a length of 0.5 m at 100 ° C . The rod is cooled to 0 ° C but preven

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100

A wire fixed to the ceiling at one end is being pulled slowly by a force F at the other end. If the change in length of the wire is l , then the work done by the force F is

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101

The elastic limit of brass is 379 M P a . The minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit will be

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102

A heavy plank of mass 100 kg hangs on three vertical wires of equal length arranged symmetrically (see figure). All the wires have the same cross-section. The middle wire is of ste

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103

Two blocks of masses 5 kg and 10 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal wire is 2 × 10 9 N m - 2 . If

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104

A bottle has an opening of radius a and length b . A cork of length b and radius a + ∆ a where ∆ a ≪ a , is compressed to fit into the opening completely (see figure). If the bulk

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105

A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm . Then the elastic energy store

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106

There is no change in the volume of a wire due to the change in its length on stretching. The Poisson's ratio of the material of the wire is

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107

A body of mass m = 10 k g is attached to one end of a wire of length 0.3 m . What is the maximum angular speed (in r a d s - 1 ) with which it can be rotated about its other end in

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108

A steel rod is projecting out of a rigid wall. The shearing strength of steel is 345 MN m - 2 . The dimensions AB = 5 cm , BC = BE = 2 cm . The maximum load that can be put on the

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109

The length of an elastic string is a m when the tension is 4 N , and ' b m when the tension is 5 N . The length in metre when the tension is 9 N , is

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110

The longitudinal stress in a rod (with rectangular cross-section) is 1 % of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisso

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111

A sphere of radius 0 . 1   m and mass 8 π  kg is attached to the lower end of a steel wire of length 5 . 0   m & diameter 10 - 3   m . The wire is suspende

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112

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant k . A mass m hangs freely from the free end of the

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113

A rigid bar of mass 15 kg is supported symmetrically by three wires, each of length 2 m . The wires at the endpoints are made of copper and the middle one is made of steel. If the

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114

The pressure applied from all directions on a cube is p . How much its temperature should be raised to maintain the original volume? The volume elasticity of the cube is β and the

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115

The length of a metal wire is l 1 when the tension in it is T 1 and is l 2 when the tension is T 2 . The natural length of wire is

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116

A wire of cross-sectional area A is stretched horizontally between two clamps loaded at a distance 2 l metres from each other. A weight w kg suspended from the midpoint of the wire

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117

When a metallic wire is held under a tensile force F 1 , the length of the wire is L 1 . If the force is changed to F 2 , the length of the wire is L 2 . The original length L of t

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118

A load of 31 . 4 kg is suspended from a wire of radius 10 - 3 m and density 9 × 10 3 kg m - 3 . Calculate the change in temperature of the wire if 75 % of the stored elastic potent

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119

32 g of O 2 is contained in a cubical container of side 1 m and maintained at a temperature of 127 ° C . The isothermal bulk modulus of elasticity of the gas is (universal gas cons

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120

There is some change in length when a 33000 N tensile force is applied on a steel rod of the area of cross-section 10 - 3 m 2 . The change of temperature required to produce the sa

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