A) \[55\,m\]
B) \[110\,m\]
C) \[220\,m\]
D) \[230\,m\]
Correct Answer: C
Solution :
| [c] Let \[{{R}_{1}}\] and \[{{R}_{2}}\] be the radii of outer and inner circular path respectively. |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\frac{2\pi {{R}_{1}}}{2\pi {{R}_{2}}}=\frac{23}{22}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{23}{22}\,\,\,\,\,\,\,\Rightarrow \,\,{{R}_{1}}=\frac{23}{22}{{R}_{2}}\] (1) |
| Also,\[{{R}_{1}}-{{R}_{2}}=5\,\,\,\,\Rightarrow \,\,\,\frac{23}{22}{{R}_{2}}-{{R}_{2}}=5\](Using (1)) |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,{{R}_{2}}=5\times 22=110m\] |
| \[\therefore \] Diameter of inner circle \[=2{{R}_{2}}=(2\times 110)\,m=220m\] |
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