Mechanical Properties of Solids

A wire of length 2 m and cross-sectional area 1 × 10⁻⁶ m² is stretched by a force of 100 N. If the Young's modulus of the material is 2 × 10¹¹ N/m², find the elongation produced.

Two wires of the same material have lengths in the ratio 2 : 1 and radii in the ratio 1 : 2. If both are stretched by the same force, find the ratio of their elongations.

The breaking stress of a given wire does NOT depend upon:

A steel wire has a breaking stress of 8 × 10⁸ N/m² and density 8 × 10³ kg/m³. Find the maximum length of this wire that can hang vertically without breaking under its own weight. (g = 10 m/s²)

A rubber cord of natural length 0.5 m and cross-sectional area 2 × 10⁻⁶ m² (Young's modulus 5 × 10⁸ N/m²) is stretched by 1 cm. Find the elastic potential energy stored in it.

When the pressure on a given mass of liquid is increased by 2 × 10⁶ Pa, its volume decreases by 0.05%. Calculate the bulk modulus of the liquid.

The compressibility of a liquid is 5 × 10⁻¹⁰ Pa⁻¹. What is its bulk modulus?

A cube of side 20 cm has its bottom face fixed. A tangential force of 4000 N is applied to its top face, producing a shearing strain of 0.01. Find the modulus of rigidity of the material.

A wire is stretched so that its longitudinal strain is 1 × 10⁻³ while its lateral strain (decrease in diameter ÷ original diameter) is 3 × 10⁻⁴. Find the Poisson's ratio of the material.

The Young's modulus of a material is 2 × 10¹¹ N/m² and its Poisson's ratio is 0.25. Find its modulus of rigidity.

The Young's modulus of a material is 3 × 10¹¹ N/m² and its Poisson's ratio is 1/3. Find its bulk modulus.

On a stress–strain graph for a ductile material, the region beyond the elastic limit (where the material no longer returns to its original dimensions on unloading) but before fracture is called the:

Two wires A and B of the same length and same cross-sectional area, but different materials, are loaded identically. On their load–extension graphs, the line for wire A has a steeper slope than that for wire B. Which is correct?

As the temperature of a metal wire is increased, its Young's modulus generally:

The Young's modulus of a metal is 1 × 10¹¹ N/m² and the interatomic spacing in it is 3 × 10⁻¹⁰ m. Find the interatomic force constant.

A crane is to lift a maximum load of 5000 kg using a steel cable. If the yield strength of the steel is 2.5 × 10⁸ N/m², find the minimum cross-sectional area needed for the cable. (g = 10 m/s²)

A wire is stretched such that the stress developed is 2 × 10⁸ N/m², and the Young's modulus of the material is 2 × 10¹¹ N/m². Find the elastic energy stored per unit volume of the wire.

A cylindrical rod of length 50 cm and radius 1 cm, fixed at one end, is twisted through an angle of 0.6 rad at the free end. Find the angle of shear produced at the surface of the rod.