Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100^oC, while the other one is at 0^oC. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is

Two non-mixing liquids of densities $$\rho $$ and n$$\rho $$ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length $$\rho $$L ($$\rho $$ < 1) in the denser liquid. The density d is equal to

Coefficient of linear expansion of brass and steel rods are $$\alpha $$₁ and $$\alpha $$₂. Lengths of brass and steel rods are $$l$$₁ and $$l$$₂ respectively. If ($$l$$₁ $$-$$ $$l$$₂) is maintained same at all temperatures, which one of the following relations holds good?

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h [Latent heat of ice is $$3.4 \times {10^5}$$ J/kg and g = 10 N/Kg]