Mechanical Properties of Solids

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)

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 .

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 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 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 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 .

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).

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.

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 this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be . [Area of cross section of wire =0.005 cm2, Y=2 1011 Nm-2 and g=10 ms-2]

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 =103 kgm-3, Bulk modulus of rubber =9 108 Nm-2, and g=10 ms-2)

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 metal is 2.0 1011 N/m2. The longitudinal strain developed in the wire is 1 . The value of is . [Use g=10 m/s2] [figure]

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area 0.005 cm2 and Young's modulus 2 1011 N m-2. Neglecting friction, the longitudinal strain on wire B is 10-4. (Take g=10 m/s2) [figure]

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 F1 is applied to P, an extension of l is produced. The force which is required to produce same extension in Q is F2. The value of F1F2 is .

If average depth of an ocean is 4000 m and the bulk modulus of water is 2 109 N m-2, then fractional compression VV of water at the bottom of ocean is 10-2. The value of is (Given, g = 10 m s-2, = 1000 kg m-3)