$A$ pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is $5 \ s$ fast each day at a temperature of $15 \ ^oC$ and $10 \ s$ slow at a temperature of $30 \ ^oC$. The temperature at which it is designed to give correct time is ........ $^oC$.

$A$ block of steel of mass $2 \,kg$ slides down a rough inclined plane of inclination $\sin ^{-1}\left(\frac{3}{5}\right)$ at a constant speed. Assuming that the mechanical energy lost due to friction is used to increase the temperature of the block, calculate the rise in temperature of the block as it slides through $80 \,cm$. (Specific heat capacity of steel $= 420 \,J kg^{-1} K^{-1}$ and acceleration due to gravity $= 10 \,ms^{-2}$) (in $^{\circ} C$)

If two balls of the same metal weighing $5\, g$ and $10\, g$ strike a target with the same velocity,and the heat energy developed is used solely for raising their temperature,then the temperature rise will be higher:

$A$ 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

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

$A$ closed bottle containing water at $30^{\circ}C$ is carried to the moon in a spaceship. If it is placed on the surface of the moon,what will happen to the water as soon as the lid is opened?