Physics Mechanical Properties of Solids

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $\mathrm{W}$  attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is:

Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is---------.

An object is located at 2 km beneath the surface of the water. If the fractional compression ΔV/V is 1.36%, the ratio of hydraulic stress to the corresponding hydraulic strain will be ---------.
[Given: density of water is 1000 kgm⁻³ and g = 9.8 ms⁻².]

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is 27/8 w.r.t water, the value of r is.

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = 8 * 10¹⁰ Pa)

Speed of a transverse wave on a straight wire (mass $6.0\mathrm{g}$ $$ , length $60\mathrm{c}\mathrm{m}$ $$ and area of cross- section $1.0{\mathrm{m}\mathrm{m}}^2$ ${}^{}$ ) is $90{\mathrm{m}\mathrm{s}}^{-1}$ ${}^{}$ . If the young's modulus of wire is $16*{10}^{11}{\mathrm{N}\mathrm{m}}^{-2}$ ${}^{}{}^{}$ , the extension of wire over its natural length is:

A stone of mass 20g is projected from a rubber catapult of length 0.1m and area of cross section 10? m² stretched by an amount 0.04 m. The velocity of the projected stone is _______ m/s. (Young's modulus of rubber = 0.5 * 10? N/m²)

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y? and Y?. The combination behaves as a single wire then its Young's modulus is :