$A$ sphere of ice at $0^{\circ}C$ having initial radius $R$ is placed in an environment having ambient temperature $> 0^{\circ}C$. The ice melts uniformly,such that the shape remains spherical. After a time $t$,the radius of the sphere has reduced to $r$. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment,which graph best depicts $r(t)$?

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:

$A$ mass $m$ of material exists in its solid state at its melting temperature $0^\circ C$. The following processes occur to the material:
Process-$1$: An amount of thermal energy $Q$ is added to the material, and $\frac{2}{3}$ of the material melts.
Process-$2$: An identical additional amount of thermal energy $Q$ is added to the material, and the material is now a liquid at $40^\circ C$.
What is the ratio of the latent heat of fusion $(L)$ to the specific heat of the liquid $(s)$ for this material?

$A$ beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha$. It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha$. If now the beaker along with its contents is uniformly heated through a small temperature $T$,the level of liquid will reduce by (given $\alpha T << 1$):

$2 \ kg$ 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 $= 80 \ cal/g$)

$22320 \ cal$ of heat is supplied to $100 \ g$ of ice at $0^{\circ} C$. If the latent heat of fusion of ice is $80 \ cal \ g^{-1}$ and latent heat of vaporization of water is $540 \ cal \ g^{-1}$, the final amount of water thus obtained and its temperature respectively are: