$A$ sphere contracts in volume by $0.01 \%$ when taken to the bottom of a sea $1 \,km$ deep. Find the Bulk modulus of the material of the sphere in $N/m^2$.

The normal density of a material is $\rho$ and its bulk modulus of elasticity is $K$. The magnitude of increase in density of the material,when a pressure $P$ is applied uniformly on all sides,will be

$A$ sample of a liquid is kept at $1 \ atm$. It is compressed to $5 \ atm$,which leads to a change of volume of $0.8 \ cm^3$. If the bulk modulus of the liquid is $2 \ GPa$,the initial volume of the liquid was . . . . . . litre. (Take $1 \ atm = 10^5 \ Pa$)

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:

$A$ 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 the temperature of a gas is $20^{\circ} C$ and pressure is changed from $P_1 = 1.01 \times 10^5 \, Pa$ to $P_2 = 1.165 \times 10^5 \, Pa$,the volume changes by $10 \%$. The Bulk modulus is ......... $\times 10^5 \, Pa$.