The coefficient of apparent expansion of mercury in a glass vessel is $153\times 10^{-6}/\,^oC$ and in a steel vessel is $144\times 10^{-6}/\,^oC.$ If $\alpha $ for steel is $12 \times 10^{-6}/\,^oC,$ then $\alpha $ that of glass is

A small quantity, mass $m$ , of water at a temperature $\theta $ (in $^oC$ ) is poured on to a large mass $M$ of ice which is at its melting point. If $c$ is the specific heat of water and $L$ the latent heat of fusion of ice, then the mass of ice melted is given by

‘Stem Correction’ in platinum resistance thermometers are eliminated by the use of

A rod is fixed between two points at $20\,^oC$ . The coefficient of linear expansion of material of rod is $1.1 \times 10^{-5}/\,^oC$ and Young's modulus is $1.2 \times 10^{11}\,N/m^2$. Find the stress developed in the rod if temperature of rod becomes $10\,^oC$

A lead bullet at $27\,^oC$ just melts when stopped by an obstacle. Assuming that $25\%$ of heat is absorbed by the obstacle, then the velocity of the bullet at the time of striking is  ........ $m/s$ ( $M.P.$ of lead = $327\,^oC$, specific heat of lead $= 0.03\,cal/g\,^oC$, latent heat of fusion of lead $= 6\,cal/g$ and $J = 4.2\,joule/cal$ )

A substance of mass $m\,kg$ requires a power input of $P$ $watt$ to remain in the molten state at its melting point. When the power is turned off, the substance completely solidifies in time $t\,sec$. The latent heat of fusion of the substance is