$A$ 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,then the quantity of ice that melts is (Acceleration due to gravity $= 10 \ m/s^2$,Latent heat of ice $= 3.5 \times 10^5 \ J/kg$)

$A$ steel pendulum clock manufactured at $32^{\circ} C$ and working at $47^{\circ} C$ is nearly (Coefficient of linear expansion of steel $= 12 \times 10^{-6} /{ }^{\circ} C$)

$A$ waterfall is $84 \ m$ high. If half of the potential energy of the falling water gets converted to heat,the rise in temperature of the water will be: (in $^\circ C$)

$A$ 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 $L = 80\, cal/g = 80 \times 10^3\, cal/kg$)

$A$ hunter fired a metallic bullet of mass $m \ kg$ from a gun towards an obstacle and it just melts when it is stopped by the obstacle. The initial temperature of the bullet is $300 \ K$. If $\frac{1}{4}$ th of the heat is absorbed by the obstacle,then the minimum velocity of the bullet is (Melting point of bullet $= 600 \ K$,Specific heat of bullet $= 0.03 \ cal \ g^{-1} {}^{\circ} C^{-1}$,Latent heat of fusion of bullet $= 6 \ cal \ g^{-1}$) (in $ms^{-1}$)

An iron rod of heat capacity $C$ is heated to temperature $8T_0$. It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as a diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$. The cylinder with the piston combined have a heat capacity $2C$. Find the equilibrium temperature. (Assume the temperature of air to be uniform and equal to the vessel at all times).