$A$ 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

Bulk modulus of water is $2 \times 10^9 \ N/m^2$. The pressure required to increase the volume of water by $0.1 \%$ in $N/m^2$ is:

If the pressure of a gas is given by $P = P_0 e^{\alpha V}$,what is the bulk modulus?

The Bulk Modulus for an incompressible liquid is

$A$ sample of a liquid has an initial volume of $1.5\,L$. The volume is reduced by $0.2\,mL$ when the pressure increases by $140\,kPa$. What is the bulk modulus of the liquid?

$A$ bottle has an opening of radius $a$ and length $b$. $A$ cork of length $b$ and radius $(a + \Delta a)$,where $(\Delta a << a)$,is compressed to fit into the opening completely (see figure). If the bulk modulus of the cork is $B$ and the frictional coefficient between the bottle and the cork is $\mu$,then the force needed to push the cork into the bottle is: