A) The hollow sphere will cool at a faster rate for all values of \[T\]
B) The solid sphere will cool at a faster rate for all values of \[T\]
C) Both spheres will cool at the same rate for all values of \[T\]
D) Both spheres will cool at the same rate only for small values of \[T\]
Correct Answer: A
Solution :
Rate of cooling \[\frac{\Delta \theta }{t}=\frac{A\varepsilon \sigma ({{T}^{4}}-T_{0}^{4})}{mc}\] As surface area, material and temperature difference are same, so rate of loss of heat is same in both the spheres. Now in this case rate of cooling depends on mass. Þ Rate of cooling \[\frac{\Delta \theta }{t}\propto \frac{1}{m}\] Q \[{{m}_{solid}}>{{m}_{hollow}}\]. Hence hollow sphere will cool fast.
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