A) 4 : 5
B) 5 : 4
C) 25 : 1
D) 1 : 25
Correct Answer: D
Solution :
Heat\[Q=\frac{KA(\Delta \theta )t}{l}\] \[\because \]\[Q\]and \[\Delta \theta \] are same for both spheres hence \[\Rightarrow \] \[\frac{{{K}_{\text{larger}}}}{{{K}_{\text{smaller}}}}=\frac{{{l}_{1}}}{{{l}_{2}}}\times {{\left( \frac{{{r}_{s}}}{{{l}_{1}}} \right)}^{2}}\times \frac{{{t}_{s}}}{{{t}_{l}}}\] It is given that\[{{r}_{1}}=2{{r}_{s}},\,\,{{l}_{l}}=\frac{1}{4}{{l}_{s}}\]and\[{{t}_{l}}=25\min \] \[{{t}_{s}}=16\min \] \[\Rightarrow \] \[\frac{{{K}_{\text{larger}}}}{{{K}_{\text{smaller}}}}=\left( \frac{1}{4} \right){{\left( \frac{1}{2} \right)}^{2}}\times \frac{16}{25}=\frac{1}{25}\]
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