• # question_answer Two spheres of radii in the ratio 1 : 2 and densities in the ratio 2 : 1 and of same specific                 heat, are heated to same temperature and                 left in the same surrounding. Their rate of cooling will be in the ratio : A)  2 : 1                       B)         1 : 1 C)  1 : 2                       D)         1 : 4

The formula for rate of cooling is given by $=\frac{mc}{t}$ As, mass = volume density Mass of sphere $=\frac{4}{3}\pi {{r}^{3}}\times \rho ,$ where p is density Mass per unit area$\frac{\frac{4}{3}\pi {{r}^{3}}\times \rho }{4\pi {{r}^{2}}}=\frac{1}{3}rp$ Hence, rate of cooling per unit area must be proportional to $rp$ (here r is the radius of sphere and $\rho$ is the density. Hence, ratio of rate of cooling for two spheres is $=\frac{{{r}_{1}}\rho }{{{r}_{2}}{{\rho }_{2}}}$ where${{r}_{1}}:{{r}_{2}}\,=1:2$and${{\rho }_{1}}:{{\rho }_{2}}=2:1$                                                       $=\frac{{{r}_{1}}{{\rho }_{1}}}{{{r}_{2}}{{\rho }_{2}}}$