The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is $1 : 4$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?

$A$ 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).

$A$ 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?

$A$ 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.)

$2 \ kg$ of ice at $-20^{\circ} C$ is mixed with $5 \ kg$ of water at $20^{\circ} C$. What is the final amount of water in the mixture (in $kg$)? (Given: specific heat of ice $= 0.5 \ cal/g^{\circ} C$,specific heat of water $= 1 \ cal/g^{\circ} C$,latent heat of fusion of ice $= 80 \ cal/g$)

$A$ block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to $3\, kg$ of water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container,which of the following is true?