The Marina trench is located in the Pacific Ocean, and at one place it

1.	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?
Answer» Pressure at bottom ’of the trench = ρgh = 1.1 × 10⁸ Pa Initial volume of the ball = 0.32 m³ Bulk modulus of steel = 1.6 × 10¹¹ Pa Let ∆v the change in volume of Ball when it falls down to the bottom. We know that, B = \(\frac{p}{(ΔV/V)}\) ⇒ ∆v = \(\frac {PV}{B}\) = \(\frac{1.1 \times 10^8 \times 0.32}{1.6 \times 10^{11}}\) = 2.2 × 10^-4m³ Therefore, change in volume of the ball on reaching the bottom of the trench is 2.2 × 10^-4 m3 or 220 cm³.

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?

Answer»

Pressure at bottom ’of the trench = ρgh = 1.1 × 10⁸ Pa

Initial volume of the ball = 0.32 m³

Bulk modulus of steel = 1.6 × 10¹¹ Pa

Let ∆v the change in volume of Ball when it falls down to the bottom.

We know that, B = \(\frac{p}{(ΔV/V)}\)

⇒ ∆v = \(\frac {PV}{B}\)

= \(\frac{1.1 \times 10^8 \times 0.32}{1.6 \times 10^{11}}\)

= 2.2 × 10^-4m³

Therefore, change in volume of the ball on reaching the bottom of the trench is 2.2 × 10^-4 m3 or 220 cm³.