A) \[\text{128 cm}\]
B) \[\text{126 cm}\]
C) \[\text{63 cm}\]
D) \[\text{64 cm}\]
Correct Answer: B
Solution :
| [b] Let \[{{r}_{1}}\,cm\] and \[{{r}_{2}}\,cm\] be the radii of smaller and bigger wheels of the tractor respectively. |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{1}}+{{r}_{2}}=98\] ...(1) |
| Also, \[2\pi {{r}_{2}}-2\pi {{r}_{1}}=176\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{2}}-{{r}_{1}}=\frac{176}{2\pi }=\frac{176\times 7}{2\times 22}=28\] ...(2) |
| Adding (1) and (2), we have |
| \[2{{r}_{2}}=126\,\,\,\,\Rightarrow \,\,{{r}_{2}}=63\] |
| \[\therefore \] Diameter of bigger wheel |
| \[=(2\times 63)cm=126cm\] |
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