$A$ certain pressure $P$ is applied to $1 \text{ litre}$ of water and $2 \text{ litre}$ of a liquid separately. Water gets compressed to $0.01 \%$ whereas the liquid gets compressed to $0.03 \%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ is $...........$

$A$ cubical solid aluminium (bulk modulus $B = -V \frac{dP}{dV} = 70 \text{ GPa}$) block has an edge length of $1 \text{ m}$ on the surface of the earth. It is kept on the floor of a $5 \text{ km}$ deep ocean. Taking the average density of water $\rho = 10^3 \text{ kg m}^{-3}$ and the acceleration due to gravity $g = 10 \text{ m s}^{-2}$,the change in the edge length of the block in $\text{mm}$ is . . . . .

When a rubber ball is taken to the bottom of a sea of depth $1400 \,m$,its volume decreases by $2 \%$. The Bulk modulus of the rubber ball is .................. $\times 10^8 \,N/m^2$ [density of water is $1 \,g/cc$ and $g=10 \,m/s^2$].

$A$ spherical ball contracts in volume by $0.02 \%$,when subjected to a normal uniform pressure of $50$ atmosphere. The Bulk modulus of its material is ............... $N / m^2$.

The compressibility of water is $5 \times 10^{-10} \ m^2/N$. $A$ pressure of $15 \times 10^6 \ Pa$ is applied on $100 \ ml$ volume of water. The change in the volume of water is:

$A$ rubber ball is taken into the deep sea such that its volume decreases by $x \%$. The bulk modulus of rubber is $K$ and the density of sea water is $\rho$. The depth $h$ to which the rubber ball is taken is proportional to $(g = \text{acceleration due to gravity})$: