What is the length of a wire that breaks under its own weight when suspended vertically? Breaking stress = 5 x 10⁷ Nm^-2 and density of the material of the wire = 3 x 10³ kg/m³

Two wires of equal cross-section but one made of steel and the other copper are joined end to end. When the combination is kept under tension, the elongation in the two wires is found to be equal. Given Young's moduli of steel and copper are 2.0 x 10¹¹ Nm^-2 and 1.1 x 10¹¹Nm^-2 Find the ratio between the lengths of steel and copper wires

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm² . Calculate the elongation of the wire when the mass is at the lowest point of its path.

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column. Young's modulus, \(\Upsilon \) = 2.0 x 10¹¹ Pa.

What is the density of water at a depth where pressure is 80.0 atm, given that its density at the surface is 1.03 × 10³ kg m^–3?

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in figure. The cross-sectional areas of wires A and Bare 1.0 mm? and 2.0 mm², respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

Determine the poission's ratio of the material of wire whose volume remains constant under an external normal stress.

What do you understand by Poisson's ratio? Find the value of Poisson's ratio at which the volume of a wire does not change when the wire is subjected to a tension.

A boy's catapult is made of a rubber cord 42 cm long and 6 mm in diameter. The boy stretches the cord by 20 cm. Find the Young's modulus of the rubber if a stone weighing 0.02 kg when catapulated flies with a velocity of 20 ms^-1. Disregard the change in the cross-section of the cord in stretching.