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

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

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

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

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

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

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

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

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

Young's modulus 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 modulus will be :

1. 4 Y
2. 2 Y
3. Y4
4. Y

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 are reduced to half of their original values keeping original length constant, the increase in length will become:

1. 2 times
2. 4 times
3. 3 times
4. 32 times

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

1. (A) is false but (R) is true
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. Both (A) and (R) are true and (R) is the correct explanation of (A)
4. (A) is true but (R) is false