Specific heat capacity, calorimetry, change of state, latent heat

The quantities of heat required to raise the temperature of two solid copper spheres of radii \(r_1\) and \(r_2\) (\(r_1 = 1.5\,r_2\)) through 1 K are in the ratio :

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 is : [Latent heat of ice is \(3.4\times10^{5}\) J/kg and g = 10 N/kg]

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