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 \(1~\text{K}\) are in the ratio:
1. \(\frac{9}{4}\)
2. \(\frac{3}{2}\)
3. \(\frac{5}{3}\)
4. \(\frac{27}{8}\)

A deep rectangular pond of surface area A, containing water (density = \(\rho,\) specific heat capacity = \(s\)), is located in a region where the outside air temperature is at a steady value of \(-26^{\circ}\mathrm{C}\)$$. The thickness of the ice layer in this pond at a certain instant is \(x\). Taking the thermal conductivity of ice as \(k\), and its specific latent heat of fusion as \(L\), the rate of increase of the thickness of the ice layer, at this instant, would be given by:
1. \(\frac{26k}{x\rho L-4s}\)
2. \(\frac{26k}{x^2\rho L}\)
3. \(\frac{26k}{x\rho L}\)
4. \(\frac{26k}{x\rho L+4s}\)