Mechanical Properties of Solids

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 108 N/m2 and its radius is 4 mm, then maximum acceleration the lift can take is m/s2. (take g = 10 m/s2 and =3.14)

1. 2.56
2. 3.89
3. 4.32
4. 5.16

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 kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is m.

1. 1.1
2. 2.22
3. 1.21
4. 4.44

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-sectional area of the wire is 10-5 m2 then the Young's modulus of the wire is N/m2. [figure]

1. 1.0 1011
2. 2.0 1010
3. 1.0 1010
4. 2.0 1011

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

1. increases by two times
2. reduces by half
3. remains unchanged
4. becomes one fourth

Two wires as shown in the figure below, made of steel and have breaking stress of 12 108 N/m2. Area of cross-section of upper wire is 0.008 cm2 and of lower wire is 0.004 cm2. The maximum mass that can be added to pan without breaking any wire is kg. [figure]

1. 56
2. 38
3. 96
4. 5.6

A cube has side length 5 cm and modulus of rigidity 105 N/m2. The displacement produced by a force of 10 N in the upper face of cube is mm.

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 m3. The elastic potential energy stored in the wire in stretched condition would be J. (Given Young modulus of copper = 1.1 1011 N/m2)

The increase in the pressure required to decrease the volume ( V) of water is 6.3 107 N/m2. The percentage decrease in the volume is . (Bulk modulus of water =2.1 109 N/m2.)

1. 2 %
2. 3 %
3. 6 %
4. 4 %

A string A of length 0.314 m and Young's modulus 2 1010 N/m2 is connected to another string B of length and Young's modulus both twice of those of A. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass 0.8 kg. The net change in length of the combination is mm. (radius of both the strings is 0.2 mm and acceleration due to gravity = 10 m/s2) (Mass of both strings is to be neglected as compared to the mass of load)

1. 3
2. 2
3. 1.9
4. 1

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 using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli (YA/YB ) is 0.5. The ratio of elongations in A to B is .

1. 1
2. 4
3. 8
4. 6

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 l3 distance from the top is ( WA+ 2 wA ), where A is the cross sectional area of the wire. The value of is .

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 m2 and 4.5 10-5 m2, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is

1. 2
2. 1
3. 4
4. 5

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

1. B
2. A
3. D
4. C

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 the wire as per this experiment is P 1011 N m-2, where the value of P is: (Take g = 3 m/s2)

1. 2.5
2. 25
3. 10
4. 5

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to a change of volume of 0.8 cm3. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was litre. (Take 1 atm = 105 Pa)

Two wires A and B are made of same material having ratio of lengths LALB = 13 and their diameters ratio dAdB = 2. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

1. 3 : 4
2. 1 : 12
3. 1 : 3
4. 1 : 6

Two slabs with square cross section of different materials (1, 2) with equal sides (l) and thickness d1 and d2 such that d2 = 2d1 and l > d2. Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is 2 = 2 1. If the shear modulus of material 1 is 4 109 N/m2, then shear modulus of material 2 is x 109 N/m2, where value of x is .

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of 105 N at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement of the rod axis from its original position would be : (shear modulus, G = 1010 N/m2)

1. 1/160
2. 1/2
3. 1/4
4. 1/40

A steel wire of length 2 m and Young's modulus 2.0 1011 N m-2 is stretched by a force. If Poisson's ratio and transverse strain for the wire are 0.2 and 10-3 respectively, then the elastic potential energy density of the wire is 105 (in SI units).

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is m.

The fractional compression ( VV ) of water at the depth of 2.5 km below the sea level is %. Given, the Bulk modulus of water = 2 109 N m-2, density of water = 103 kg m-3, acceleration due to gravity g = 10 m s-2.

1. 1.0
2. 1.25
3. 1.75
4. 1.5

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of 7 106 Pa, would be mm3. (Given bulk modulus of copper = 1.4 1011 N m-2)

The increase in pressure required to decrease the volume of a water sample by 0.2\% is P 105 Nm-2. Bulk modulus of water is 2.15 109 Nm-2. The value of P is .

A massless spring gets elongated by amount x1 under a tension of 5 N. Its elongation is x2 under the tension of 7 N. For the elongation of (5x1-2x2), the tension in the spring will be,

1. 20 N
2. 39 N
3. 11 N
4. 15 N

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 wire is 2 m and the area of cross section is 2 cm2. The wire will extend in length by .

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 middle it sags lower from its original position making angle = 1100 radian on the points of support. The value of A is 10-4 m2 (consider x L). (given : g = 10 m/s2) [figure]

The density and breaking stress of a wire are 6 104 kg/m3 and 1.2 108 N/m2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 13rd of the value on the surface of earth. The maximum length of the wire without breaking is m (take, g = 10 m/s2).

Match List I with List II : Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
2. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
3. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
4. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

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

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

1. changes erratically
2. increases
3. decreases
4. remains unchanged