$500\, g$ of water and $100\, g$ of ice at $0\,^{\circ}C$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^{\circ}C$ is added to it. Then the final amount of water in the calorimeter is ....... $g$ (Latent heat of ice $= 80\, cal/g$,Latent heat of steam $= 540\, cal/g$).

$A$ lead bullet at $27^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,find the velocity of the bullet at the time of striking in $m/s$. (Melting point of lead $= 327^{\circ}C$,specific heat of lead $= 0.03 \, cal/g^{\circ}C$,latent heat of fusion of lead $= 6 \, cal/g$,and $J = 4.2 \, J/cal$)

$A$ piece of ice (heat capacity = $2100 \text{ J kg}^{-1} \text{ }^\circ\text{C}^{-1}$ and latent heat = $3.36 \times 10^5 \ J kg^{-1}$) of mass $m$ grams is at $-5^oC$ at atmospheric pressure. It is given $420 \ J$ of heat so that the ice starts melting. Finally, when the ice-water mixture is in equilibrium, it is found that $1 \ gm$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is ...... $gm$.

Column $I$ gives some devices and Column $II$ gives some processes on which the functioning of these devices depends. Match the devices in Column $I$ with the processes in Column $II$.

Column $I$	Column $II$
$(A)$ Bimetallic strip	$(p)$ Radiation from a hot body
$(B)$ Steam engine	$(q)$ Energy conversion
$(C)$ Incandescent lamp	$(r)$ Melting
$(D)$ Electric fuse	$(s)$ Thermal expansion of solids

$A$ copper ring has a diameter of exactly $25 \, mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05 \, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and the two are allowed to come to thermal equilibrium,with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere to the ring is: (Given: $\alpha_{Cu} = 17 \times 10^{-6} /^o C$,$\alpha_{Al} = 2.3 \times 10^{-5} /^o C$,specific heat of $Cu = 0.0923 \, cal/g^o C$,and specific heat of $Al = 0.215 \, cal/g^o C$)

Water is fully filled in a container at $4^{\circ}C$. What happens to the water level when the temperature changes?