Data:-

h=200 m, dv=0.1%

To find:- k=?

Solution:-

Increase in pressure on ball

$d_p=W_w\times h$

$=9810\times 200$

$1.96\times 10^6 N/m^2$

Also,

Decrease in volume = 0.1%

$-\frac{dv}{v}=\frac{0.1}{100}$

Bulk Modulus (k)

$k=\frac{dP}{-\frac{dv}{v}}=\frac{1.962\times 10^6}{\frac{0.1}{100}}$

$k=1.962\times 10^9 N/m^2$