The densities of wood and benzene at $0^{\circ} C$ are $880 \ kg \ m^{-3}$ and $900 \ kg \ m^{-3}$,respectively. The coefficients of volume expansion are $1.2 \times 10^{-3} \ ^{\circ}C^{-1}$ for wood and $1.5 \times 10^{-3} \ ^{\circ}C^{-1}$ for benzene. The temperature at which a piece of wood just sinks in benzene is (in $^{\circ} C$)

$A$ hammer of mass $200 \ kg$ strikes a steel block of mass $200 \ g$ with a velocity $8 \ ms^{-1}$. If $23 \%$ of the energy is utilized to heat the steel block,the rise in temperature of the block is (specific heat capacity of steel,$s = 460 \ J \ kg^{-1} \ K^{-1}$) (in $K$)

$A$ cylinder of mass $1\,kg$ is given heat of $20000\,J$ at atmospheric pressure. If the initial temperature of the cylinder is $20\,^oC$,then the work done by the cylinder will be .......$J$. (Given: Specific heat of cylinder $= 400\,J\,kg^{-1}\,^oC^{-1}$,Coefficient of volume expansion $= 9 \times 10^{-5}\,^oC^{-1}$,Atmospheric pressure $= 10^5\,N/m^2$,and density of cylinder $= 9000\,kg/m^3$)

The figure shows a glass tube (linear coefficient of expansion is $\alpha$) completely filled with a liquid of volume expansion coefficient $\gamma$. On heating,the length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$.

$A$ lead bullet of $20 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50 \%$ of heat is absorbed by the bullet,the increase in its temperature is $.....^{\circ} C$ (take specific heat of lead $= 150 \ J/kg \cdot K$).

Which of the following graphs shows the variation of thermoelectric power of a thermocouple with the temperature difference between the hot and cold junctions?