$A$ lead bullet of $10\,g$ travelling at $300\,m/s$ strikes against a block of wood and comes to rest. Assuming $50\,\%$ of heat is absorbed by the bullet,the increase in its temperature is ........ $^oC$ (Specific heat of lead $= 150\,J/kg\cdot K$)

$A$ thermally insulated vessel contains some water at $0^{\circ}C$. The vessel is connected to a vacuum pump to pump out water vapour. This results in some water getting frozen. It is given that the latent heat of vaporization of water at $0^{\circ}C = 21 \times 10^5 \text{ J/kg}$ and the latent heat of fusion of water $= 3.36 \times 10^5 \text{ J/kg}$. The maximum percentage amount of water that will be solidified in this manner will be ...... $\%$

$A$ metal sphere immersed in water weighs $w_1$ at $0^{\circ} C$ and $w_2$ at $50^{\circ} C$. The coefficient of cubical expansion of the metal is less than that of water. Then

Water falls from a height of $500 \ m$. What is the rise in temperature of water at the bottom if the whole energy remains in the water? (Assume $g = 9.8 \ m/s^2$ and specific heat capacity of water $c = 4200 \ J/kg \cdot ^\circ C$)

$A$ lead bullet of mass $50 \ g$ at a temperature of $30^{\circ}C$ is fired vertically upwards with a speed of $840 \ m/s$. When the bullet returns to the point of departure,it strikes a large block of ice at $0^{\circ}C$. How much ice (in $g$) will melt? (Specific heat of lead is $0.02 \ cal/g^{\circ}C$,latent heat of fusion of ice is $80 \ cal/g$,and assume all energy is used to melt the ice.)

$A$ lead bullet moving with velocity $V$ strikes a wall and stops. If $75 \%$ of its energy is converted into heat,then the increase in temperature is ($s=$ specific heat of lead,$J=$ mechanical equivalent of heat).