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 × 10⁸ Pa. A steel ball of initial volume 0.32 m3 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?
Given, the water pressure is 1.1 × 10 8 Pa , the initial volume of the steel ball is 0.32 m 3 . The bulk modulus of steel is 1.6 × 10 11 N / m 2 .
The bulk modulus of steel is given by the equation,
B = Δ p V Δ V Δ V = Δ p V B
Substituting the values in the above expression, we get:
Δ V = 1.1 × 10 8 Pa × 0.32 m 3 1.6 × 10 11 N / m 2 ≈ 2.51 × 10 − 4 m 3
Hence, the change in volume of the ball is 2.51 × 10 − 4 m 3 .
Given, the water pressure is
The bulk modulus of steel is given by the equation,
Substituting the values in the above expression, we get:
Hence, the change in volume of the ball is
