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\[=\frac{4}{3}\pi {{r}^{3}}\times \rho ,\] where\[\rho \]is density Mass per unit area \[=\frac{\frac{4}{3}\pi {{r}^{3}}\times \rho }{4\pi {{r}^{2}}}=\frac{1}{3}r\rho \] 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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