$A$ 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 $^\circ C$)

The height of a waterfall is $50 \ m$. If $g = 9.8 \ m/s^2$, the difference between the temperature at the top and the bottom of the waterfall is: (in $^{\circ} C$)

When $1\, g$ of water at $0^{\circ}C$ and $1 \times 10^5\, N/m^2$ pressure is converted into ice of volume $1.091\, cm^3$,the external work done will be (in $, J$)

The heat required to convert $8 \ g$ of ice at a temperature of $-20^{\circ}C$ to steam at $100^{\circ}C$ is (Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$, specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$, latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$ and latent heat of steam $= 2.268 \times 10^6 \ J \ kg^{-1}$) (in $kJ$)

Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$. The specific heat of ice is $2222.3\,J\,kg^{-1\circ}C^{-1}$ and the latent heat of fusion of ice is $336\,kJ\,kg^{-1}$.
$(A)$ Final temperature of the system will be $0^{\circ}C$.
$(B)$ Final temperature of the system will be greater than $0^{\circ}C$.
$(C)$ The final system will have a mixture of ice and water in the ratio of $5:1$.
$(D)$ The final system will have a mixture of ice and water in the ratio of $1:5$.
$(E)$ The final system will have water only.
Choose the correct answer from the options given below:

$A$ copper ring has a diameter of exactly $25 \, mm$ at its temperature of $0^o C$. An aluminium sphere has a diameter of exactly $25.05 \, mm$ at its temperature of $100^o C$. The sphere is placed on top of the ring and the two are allowed to come to thermal equilibrium,with no heat being lost to the surroundings. The sphere just passes through the ring at the equilibrium temperature. The ratio of the mass of the sphere to the ring is: (Given: $\alpha_{Cu} = 17 \times 10^{-6} /^o C$,$\alpha_{Al} = 2.3 \times 10^{-5} /^o C$,specific heat of $Cu = 0.0923 \, cal/g^o C$,and specific heat of $Al = 0.215 \, cal/g^o C$)