A) 2:1
B) 1:1
C) 1 : 2
D) 1 : 4
Correct Answer: B
Solution :
The formula for rate of cooling is given by \[=\frac{mc\,\theta }{t}\] As, mass = volume \[\times \] density Mass of sphere \[=\frac{4}{3}\pi {{r}^{2}}\times \rho ,\] where \[\rho \] is density Mass per unit area \[=\frac{4}{3}\pi {{r}^{2}}=\frac{\frac{4}{3}\pi {{r}^{3}}\times \rho }{4\pi {{r}^{2}}}=\frac{1}{3}r\rho \] Hence, rate of cooling per unit area must be proportional to \[r\rho \]. (here r is the radius of sphere and p is the density. Hence, ratio of rate of cooling for two spheres Is \[=\frac{{{r}_{1}}{{\rho }_{1}}}{{{r}_{2}}{{\rho }_{2}}}\] where \[{{r}_{1}}:{{r}_{2}}=1:2\] and \[{{\rho }_{1}}:{{\rho }_{2}}=2:1\] \[=\frac{1}{2}\times \frac{2}{1}=1:1\]
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