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 × 108 Pa. A steel ball of initial volume 0.32 mis 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?

Asked by Abhisek | 1 year ago |  143

Solution :-

Water pressure at the bottom of the trench, p=1.1×10 8 Pa

Initial volume of the steel ball, V=0.32m3

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

The ball falls at the bottom of the trench which is nearly 11 km beneath the surface of the water.

The volume change of the ball after reaching the bottom of the trench is  △V

Bulk modulus, B

=$$\dfrac{p}{\dfrac{△V}{V}}$$

△V= $$\dfrac{pV}{B}$$

=$$\dfrac{(1.1×10^8×0.32)}{(1.6×10^{11})}$$

$$\dfrac{0.352 ×10^8}{1.6×10^{11}}$$

= 0.22 x 10-3m3

The change in volume of the ball on reaching the bottom of the trench is 0.22 x 10-3m3

Answered by Pragya Singh | 1 year ago

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