Ncert Exercises & Solutions

9.21 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 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?

W know:

The bulk modulus of steel = $1.6 \times 10^{11} {Nm}^{- 2}$

Let the change in the volume of the ball on reaching the bottom of the trench be $∆$ V.

Bulk modulus, B= $\frac{P}{\frac{∆ V}{V}}$

$∆ V = \frac{B}{PV}$
$= \frac{1.1 \times 10^{8} \times 0.32}{1.6 \times 10^{11}}$
$= 2.2 \times 10^{- 4} m^{3}$

Therefore, the change in volume of the ball on reaching the bottom of the trench is 2.2 × 10 $^{- 4}$ m $^{3}$ .

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