The bulk modulus of rubber is $9.1 \times 10^8 \, N/m^2$. To what depth should a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$? (Take density of water $\rho = 10^3 \, kg/m^3$ and $g = 10 \, m/s^2$)

$A$ solid sphere of radius $R$ made of a material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. $A$ massless piston of area $A$ floats on the surface of the liquid. When a mass $m$ is placed on the piston to compress the liquid,the fractional change in the radius of the sphere $\delta R/R$ 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 ......... $\times 10^5 \, Pa$.

If the compressibility of water is $\sigma$ per unit atmospheric pressure,then the decrease in volume $V$ due to $P$ atmospheric pressure will be

The density of a metal at normal pressure is $\rho$. When an additional pressure $P$ is applied,its density becomes $\rho'$. If its bulk modulus is $B$,then the ratio $\frac{\rho'}{\rho}$ is:

If a brass sphere of radius $36 \ cm$ is submerged in a lake at a depth where the pressure is $10^7 \ Pa$,then the change in the radius of the sphere is $($Bulk modulus of brass $= 60 \ GPa)$.