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Question

TheMarina trench is located in the Pacific Ocean, and at one place it isnearly eleven km beneath the surface of water. The water pressure atthe bottom of the trench is about 1.1 × 108Pa. A steel ball of initial volume 0.32 m3is dropped into the ocean andfalls to the bottom of the trench. What is the change in the volumeof the ball when it reaches to the bottom?

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Solution

Water pressure at the bottom, p = 1.1 × 108 Pa

Initial volume of the steel ball, V = 0.32 m3

Bulk modulus of steel, B = 1.6 × 1011 Nm–2

The ball falls at the bottom of the Pacific Ocean, which is 11 km beneath the surface.

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

Therefore, the change in volume of the ball on reaching the bottom of the trench is 2.2 × 10–4 m3.


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