$A$ piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is (Latent heat of ice is $L = 3.4 \times 10^{5} \text{ J/kg}$ and $g = 10 \text{ N/kg}$) (in $\text{ km}$)

$A$ stationary object at $4^{\circ}C$ and weighing $3.5\, kg$ falls from a height of $2000\, m$ on a snow mountain at $0^{\circ}C$. If the temperature of the object just before hitting the snow is $0^{\circ}C$ and the object comes to rest immediately $(g = 10\, m/s^2)$ and (latent heat of ice $= 3.5 \times 10^5\, J/kg$),then the amount of ice that will melt is:

Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

The height of Victoria Falls is $63 \ m$. What is the difference in temperature of water at the top and at the bottom of the fall? (In $^{\circ}C$)
[Given $1 \ cal = 4.2 \ J$ and specific heat of water $= 1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$]

$A$ child running a temperature of $101\,^{\circ} F$ is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to $98\,^{\circ} F$ in $20$ minutes,what is the average rate of extra evaporation caused by the drug (in $g/min$)? Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is $30\; kg$. The specific heat of the human body is approximately the same as that of water,and the latent heat of evaporation of water at that temperature is about $580\; cal \;g^{-1}$.

$A$ beaker is completely filled with water at $4 \text{ } ^\circ C$. When will the water in this beaker overflow?