A) 4 : 5
B) 5 : 4
C) 25 : 1
D) 1 : 25
Correct Answer: D
Solution :
\[Q=\frac{KA\,(\Delta \theta )t}{l}\] \[\because \] Q and \[\Delta \theta \] are same for both spheres hence \[K\propto \frac{l}{At}\propto \frac{l}{{{r}^{2}}t}\]Þ \[\frac{{{K}_{\text{larger}}}}{{{K}_{\text{smaller}}}}=\frac{{{l}_{l}}}{{{l}_{s}}}\times {{\left( \frac{{{r}_{s}}}{{{r}_{l}}} \right)}^{2}}\times \frac{{{t}_{s}}}{{{t}_{l}}}\]. It is given that \[{{r}_{l}}=2{{r}_{s}},\] \[{{l}_{l}}=\frac{1}{4}{{l}_{s}}\] and \[{{t}_{1}}=25\]min, \[{{t}_{s}}=16\]min. Þ \[\frac{{{k}_{\text{larger}}}}{{{k}_{\text{smaller}}}}=\left( \frac{1}{4} \right){{\left( \frac{1}{2} \right)}^{2}}\times \frac{16}{25}=\frac{1}{25}\]
You need to login to perform this action.
You will be redirected in
3 sec
