Mechanical Properties of Solids · Question 10

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.