A metallic wire is stretched by suspending a weight from it.If l is teh longitudinal strain and Y is the Young's Modulus,show that elastic potentially enrgy per unit volume is given by `1/2 Yl^2`.

Define Young's modulus of elasticitiy. normal stress and longitudinal strain. Give unit of each of them. Derive an expression for the elastic potential energy of a wire, when stretched.

A stell wire of length 4 m ,is stretched through 2 mm ,.The corss - sectional area of the wire is 2.0 mm^2 .If young's modulus of steel si 2.0 xx 10 ^11 N//^2 find The elastic potential energy stored in the wire.

Two wires of the same material and length but diameters in the ratio 1:2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be radio.

A steel wire of mass mu per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains < < longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m^-3 (Young's modulues Y = 2 xx 10^11 N m^-2)

A thick wire of density rho and l is hung from a rigid support .Young's modulus of the material of wire is Y.What is the increases in length of the wire due to its own weight?

In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structureslike trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by (Ypir^4)/(4R) . Y is the Young's modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neuttral surface). EStimate the critical height of a tree for a given radius of the trunk.

A beam of length'l' is suported at one end. If W is the uniform load per unit length, the bending moment M at a distance 'x' from the end is given by M =1/2 lx -1/2 Wx^2 Find the point on the beam at which the bending moment has maximum value.

A wire AB is carrying a steady current of 12A and is lying on the table. Another wire CD carrying 5A is held directly above AB at a height of 1mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10ms^-2 ]

A horizontal wire AB of length 'l' and mass 'm' carries a steady current I_1 , free to move in vertical plane is in equilibrium at a heigh of 'h' over another parallel long wire CD carrying a steady current I_2 , which is fixed in a horizontal plane as shown. Derive the expression for the force acting per unit length on the wire AB and write the condition for which wire AB is in equilibrium.

A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pilars show in the figure A mass m is suspended from the mid point of the wire. Strain in the wire is .