A) 5
B) \[\frac{5}{\pi }\]
C) \[\frac{5}{2\pi }\]
D) \[\frac{\pi }{5}\]
Correct Answer: C
Solution :
Here, we can treat the balloon as sphere. Its circumference \[=2\pi r\] \[\therefore \] \[2\pi {{r}_{1}}=20\] \[2\pi {{r}_{2}}=25\] On dividing Eq. (ii) by Eq. (i), \[\Rightarrow \] \[\frac{2\pi {{r}_{2}}}{2\pi {{r}_{1}}}=\frac{25}{20}\] \[\Rightarrow \] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{5}{4}\] \[\therefore \] Increase \[{{r}_{2}}-{{r}_{1}}\] \[=\frac{5}{4}{{r}_{1}}-{{r}_{1}}=\frac{1}{4}{{r}_{1}}=\frac{1}{4}\times \frac{20}{2\pi }\] \[=\frac{5}{2\pi }\]
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