An increase in pressure required to decrease the $200 \ L$ volume of a liquid by $0.004\%$ in a container is .......... $kPa$ (Bulk modulus of the liquid $= 2100 \ MPa$).

Find the stress developed inside a tooth cavity filled with copper when hot tea at a temperature of $57^{\circ} C$ is drunk. You can take the body (tooth) temperature to be $37^{\circ} C$ and $\alpha = 1.7 \times 10^{-5} {}^{\circ} C^{-1}$,bulk modulus for copper $B = 140 \times 10^9 \ Nm^{-2}$.

The adiabatic elasticity of a gas is equal to

$A$ solid sphere of radius $r$ made of a soft 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,covering the entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid,the fractional decrement in the radius of the sphere,$\left( \frac{dr}{r} \right)$ is:

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

$A$ 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: