Given,

Water pressure at the bottom, p = 1000 atm

= 1000 x 1.013 x 10^{5} Pa

p = 1.01 x 10^{8} Pa

Initial volume of the steel ball, V = 0.30 m^{3}

We know, bulk modulus of steel, B = 1.6 × 10^{11 }Nm^{–2}

Let the change in the volume of the ball on reaching the bottom of the trench be ΔV.

Bulk modulus, B

= \( \dfrac{p}{(∆V/V)}\)

∆V = \( \dfrac{pV}{B}\)

= \( \dfrac{1.01 × 10^8 × 0.30}{(1.6 × 10^{11 }) }\)

= 1.89 × 10^{-4} m^{3}

Hence, volume of the ball changes by 1.89 × 10^{-4} m^{3} on reaching the bottom of the trench.

A mild steel wire of cross-sectional area 0.60 x 10 ^{-2} cm^{2} and length 2 m is stretched ( not beyond its elastic limit ) horizontally between two columns. If a 100g mass is hung at the midpoint of the wire, find the depression at the midpoint.

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven km beneath the surface of the water. The water pressure at the bottom of the trench is about 1.1 × 10^{8} Pa. A steel ball of initial volume 0.32 m^{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 the bottom?

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 × 10^{7 }Pa? Assume that each rivet is to carry one-quarter of the load.

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 the figure. The cross-sectional areas of wires A and B are 1.0 mm^{2 }and 2.0 mm^{2}, 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.

Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the 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 50,000 N. What is the pressure at the tip of the anvil?