If a rubber ball is taken to a depth of $200 \ m$ in a pool,its volume decreases by $0.1 \%$. If the density of the water is $1 \times 10^3 \ kg/m^3$ and $g = 10 \ m/s^2$,then the bulk modulus (volume elasticity) in $N/m^2$ will be:

$A$ solid sphere of radius $10\,cm$ is subjected to a pressure of $5\times 10^8\,Nm^{-2}$. Determine the change in its volume. The bulk modulus of the material of the sphere is $3.14 \times 10^{11}\,Nm^{-2}$.

$1\, m^3$ of water is brought inside a lake up to a depth of $200\, m$ from the surface. What will be the change in volume if the bulk modulus of elasticity of water is $22000\, \text{atm}$? (Given: density of water $\rho = 1\times10^3\, kg/m^3$, atmospheric pressure $P_0 = 10^5\, N/m^2$, and $g = 10\, m/s^2$)

How much pressure (in atm) is needed to compress a sample of water by $0.4 \%$ (in $\text{ atm}$)? (Assume, Bulk modulus of water $\approx 2.0 \times 10^9 \text{ Pa}$)

Determine the volume contraction of a solid copper cube,$10 \; cm$ on an edge,when subjected to a hydraulic pressure of $7.0 \times 10^{6} \; Pa$.

When a rubber ball is taken to a depth of $h$ meters in deep sea,its volume decreases by $0.5\, \%$. Calculate the depth $h$. (Given: Bulk modulus of rubber $B = 9.8 \times 10^{8} \, \text{N/m}^2$,Density of sea water $\rho = 10^{3} \, \text{kg/m}^3$,$g = 9.8 \, \text{m/s}^2$)