If the pressure on a body is increased from $200 \text{ kPa}$ to $250 \text{ kPa}$,the volume of the body decreases by $0.25 \%$. The compressibility of the material of the body is (in $m^2 \text{ N}^{-1}$)

Under isothermal condition,the pressure of a gas is given by $P = aV^{-3}$,where $a$ is a constant and $V$ is the volume of the gas. The bulk modulus at constant temperature is equal to $..........\,P$.

$A$ 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:

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 ......... $\times 10^5 \, Pa$.

Calculate 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 $\alpha = 1.7 \times 10^{-5}/^{\circ}C$,bulk modulus for copper $= 140 \times 10^9\, N/m^2$.

An object is located at $2 \, km$ beneath the surface of the water. If the fractional compression $\frac{\Delta V}{V}$ is $1.36 \, \%$,the ratio of hydraulic stress to the corresponding hydraulic strain will be ......... . [Given: density of water is $1000 \, kg \, m^{-3}$ and $g = 9.8 \, m \, s^{-2}$.]