Mechanical Properties Of Solids CBSE Questions & Answers

A piece of copper having a rectangular cross-section of 15.2 mm \( \times \) 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain? Take Young's modulus of copper as 11 \( \times \) \({\rm{1}}{0^{{\rm{1}}0}}\)Pa

A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed \({\rm{1}}{0^{\rm{8}}}\) N \({{\rm{m}}^{-{\rm{2}}}}\) , what is the maximum load the cable can support?

A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.

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 \({\rm{c}}{{\rm{m}}^{\rm{2}}}\). Calculate the elongation of the wire when the mass is at the lowest point of its path.

Compute the bulk modulus of water from the following data: Initial volume = 100.0 litre, Pressure increase = 100.0 atm (1 atm = 1.013 \( \times \) \({\rm{1}}{0^{\rm{5}}}\) Pa), Final volume = 100.5 litre

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 \( \times \) \({\rm{1}}{0^{\rm{3}}}\) kg \({{\rm{m}}^{-{\rm{3}}}}\)?

Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm. Bulk modulus of glass 37 GPa.

Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 \( \times \) \({\rm{1}}{0^{\rm{6}}}\)Pa. Bulk modulus of copper 140 GPa.

How much should the pressure on a litre of water be changed to compress it by 0.10 percent? Bulk modulus of water 2.2 GPa

Anvils made of single crystals of diamond, with the shape as shown in Figure, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compression force of 50,000 N. What is the pressure at the tip of the anvil?

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminum (wire B) of equal lengths as shown in Figure. The cross-sectional areas of wires A and B are 1.0 \({\rm{m}}{{\rm{m}}^{\rm{2}}}\) and 2.0 \({\rm{m}}{{\rm{m}}^{\rm{2}}}\), respectively. At what point along the rod should a mass m be suspended in order to produce equal stresses? Take Young's modulus of steel as 200 GPa, for aluminum 70 GPa

A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminum (wire B) of equal lengths as shown in Figure. The cross-sectional areas of wires A and B are 1.0 \({\rm{m}}{{\rm{m}}^{\rm{2}}}\) and 2.0 \({\rm{m}}{{\rm{m}}^{\rm{2}}}\), respectively. At what point along the rod should a mass m be suspended in order to produce equal strains in both steel and aluminum wires. Take Young's modulus of steel as 200 GPa, for aluminum 70 GPa

A mild steel wire of length 1.0 m and cross-sectional area 0.50 \( \times \) \({\rm{1}}{0^{ - {\rm{2}}}}\) \({\rm{c}}{{\rm{m}}^{\rm{2}}}\) is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 \( \times \) \({\rm{1}}{0^{\rm{7}}}\)Pa? Assume that each rivet is to carry one quarter of the load.

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 \( \times \) \({\rm{1}}{0^{\rm{8}}}\) Pa. A steel ball of initial volume 0.32 \({{\rm{m}}^{\rm{3}}}\) is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom? Bulk modulus of steel = 160 GPa