The depth below the surface of sea to which a rubber ball be take… - Vidyadip

MCQ

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02 \%$ is______ $\mathrm{m}$.

(Take density of sea water $=10^3 \mathrm{kgm}^{-3}$, Bulk modulus of rubber $=9 \times 10^8 \mathrm{Nm}^{-2}$, and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

A
$15$
B
$16$
C
$17$
✓
$18$

✓

Answer

Correct option: D.

$18$

d
$\beta=\frac{-\Delta \mathrm{P}}{\frac{\Delta \mathrm{V}}{\mathrm{V}}}$

$\Delta \mathrm{P}=-\beta \frac{\Delta \mathrm{V}}{\mathrm{V}}$

$\rho \mathrm{gh}=-\beta \frac{\Delta \mathrm{V}}{\mathrm{V}}$

$10^3 \times 10 \times \mathrm{h}=-9 \times 10^8 \times\left(-\frac{0.02}{100}\right)$

$\Rightarrow \mathrm{h}=18 \mathrm{~m}$

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