When a rubber ball is taken to a depth of x $\times$10² m in deep sea, its volume decreases by 0.5%, , then the value of x is __________ (The bulk modulus of rubber = $9.8\times {10}^{8}N{m}^{-2};$ Density of sea water = 10³ kgm^-3 ; g = 9.8m/s²)

Given,

The bulk modulus of rubber = $9.8\times {10}^8{\mathrm{Nm}}^{-2};$ 

Density of sea water = 10³ kgm^-3 

g = 9.8m/s²

From the question we know that

$\mathrm{B}=-\frac{∆\mathrm{P}}{{\displaystyle \frac{∆\mathrm{V}}{\mathrm{V}}}}=-\frac{\mathrm{\rho gh}}{\frac{∆\mathrm{V}}{\mathrm{V}}}$

$-\frac{\mathrm{B}\frac{∆\mathrm{V}}{\mathrm{V}}}{\mathrm{\rho g}}=\mathrm{h}$

Substituting the values,

$\mathrm{h}=\frac{9.8\times {10}^8\times 0.5}{100\times {10}^3\times 9.8}=5\times {10}^2\mathrm{m}$

Hence the correct answer is 5.