$A$ lead bullet moving with velocity '$v$' strikes a wall and stops. If $50\%$ of its energy is converted into heat,then the increase in temperature is ($s =$ specific heat of lead,$J =$ mechanical equivalent of heat).

The height of a waterfall is $50 \ m$. If $g = 9.8 \ m/s^2$,the difference between the temperature at the top and the bottom of the waterfall is: (in $^{\circ} C$)

$A$ 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 $\text{ km}$)

The temperature of Bhakhra dam water at the ground level with respect to the temperature at a high level should be:

An amount of ice of mass $10^{-3} \ kg$ and temperature $-10^{\circ} C$ is transformed to vapour of temperature $110^{\circ} C$ by applying heat. The total amount of heat required for this conversion is,(Take,specific heat of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$,specific heat of water $= 4180 \ J \ kg^{-1} \ K^{-1}$,specific heat of steam $= 1920 \ J \ kg^{-1} \ K^{-1}$,Latent heat of ice $= 3.35 \times 10^5 \ J \ kg^{-1}$ and Latent heat of steam $= 2.25 \times 10^6 \ J \ kg^{-1}$) (in $J$)

$A$ gun fires a lead bullet of temperature $300 \ K$ into a wooden block. The bullet having a melting temperature of $600 \ K$ penetrates into the block and melts down. If the total heat required for the process is $625 \ J$,then the mass of the bullet is . . . . . . grams. (Latent heat of fusion of lead $= 2.5 \times 10^4 \ J \ kg^{-1}$ and specific heat capacity of lead $= 125 \ J \ kg^{-1} K^{-1}$)