Question

The Mariana trench is located in the Pacific Ocean and at one place it is nearly 11 km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 × 10⁸ Pa. A steel ball of initial volume 0.32 m 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?

(K = 1.6 × 10¹¹ N/m²)

Answer 1

Given: V = 0.32 m³, K = 1.6 × 10¹¹ N/m²,

P_W = 1.1 × 10⁸ Pa, P_atm = 1.01 × 10⁵ Pa

∴ dP = P_W – P_atm = 1.1 × 10⁸ – 1.01 × 10⁵ ≈ 1.1 × 10⁸ Pa

As, bulk modulus is given as,

K = V × \(\frac{dP}{dV}\)

∴ dV = 2.2 × 10^-4 m³

The change in the volume of the ball when it reaches the bottom will be 2.2 × 10^-4 m³.