$A$ hailstone at $0^{\circ}C$ falls from a height of $1\, km$ on an insulating surface,converting the whole of its kinetic energy into heat. What part of it will melt? (Take $g = 10\, m/s^2$,$J = 4.2\, J/cal$,and latent heat of fusion of ice $L = 80\, cal/g = 80 \times 10^3\, cal/kg$)

Match the following :

Column-$I$	Column-$II$
$(a)$ Combined existence of liquid-gaseous state of substance.	$(i)$ Sublimation curve
$(b)$ Combined existence of solid-gaseous state of substance.	$(ii)$ Fusion curve
	$(iii)$ Vaporization curve

The heat extracted out of $x \ \text{g}$ of water initially at $50^\circ \text{C}$ to cool it down to $0^\circ \text{C}$ is sufficient to evaporate $(1000 - x) \ \text{g}$ of water also initially at $50^\circ \text{C}$. The value of $x$ (closest integer) is . . . . . . . (Take latent heat of water $L = 2256 \ \text{kJ/kg}$, specific heat capacity of water $c = 4200 \ \text{J/kg}\cdot \text{K}$)

If in the winter season the surface temperature of a lake is $1^{\circ} C$,the temperature at the bottom of the lake will be ............

$A$ glass flask of volume $1$ litre is fully filled with mercury at $0\,^{\circ}C$. Both the flask and mercury are now heated to $100\,^{\circ}C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^{\circ}C$ and the coefficient of linear expansion of glass is $10 \times 10^{-6}/^{\circ}C$,the amount of mercury which is spilled out is ............ $ml$. (in $.2$)

$A$ hailstone of mass $42 \,g$ falls from a height of $1.8 \,km$. If its entire potential energy is converted into latent heat, what is the mass of the hailstone remaining when it reaches the ground (in $\,g$)? $\left(g=10 \,ms^{-2}, L_{\text{ice}}=3.36 \times 10^5 \,J \,kg^{-1}\right)$