Mechanical Properties of Solids

Why the maximum height of a mountain on earth is ~10 km.

The average depth of Red Sea is about 2000 m. Calculate the fractional compression ΔV/V of water at the bottom of the ocean, given that the bulk modulus of water is 2.2 × 10⁹ N m^-2. (Take g = 10 m s^-2)

A square copper slab of side 20 cm and thickness 5 cm is subject to a shearing force (on its narrow face) of 5.0 × 10² N. The lower edge is fixed to the floor. How much will the upper edge be displaced. G = 42 × 10⁹ N m^-2

Why steel is preferred over copper, brass and aluminium in heavy-duty machines and in structural designs.

A structural iron rod has a radius of 10 mm and a length of 1.0 m. A 1000 kN force stretches it along its length. Calculate 

(a) stress, 

(b) elongation, and 

(c) strain on the rod. Young’s modulus, of iron is 1.9 × 1011 N m–2.

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 B are 1.0 mm² and 2.0 mm², respectively.  At what point along the rod should a mass m be suspended in order to produced (a) equal stresses and (b) equal strains in both steel and aluminium wires.

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 compressional force of 50, 0000 N. What is the pressure at the tip of the anvil.