A) 4 : 1
B) 2 : 1
C) 16 : 1
D) 36 : 1
Correct Answer: D
Solution :
Centripetal acceleration is given by \[a={{\omega }^{2}}r=\frac{{{v}^{2}}}{{{r}^{2}}}\times r=\frac{{{v}^{2}}}{r}\Rightarrow a\propto \frac{{{v}^{2}}}{r}\] But given: \[{{a}_{1}}={{a}_{2}}\] \[\frac{v_{1}^{2}}{{{r}_{1}}}=\frac{v_{2}^{2}}{r_{2}^{2}}\] \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{v_{1}^{2}}{v_{2}^{2}}\] \[={{\left( \frac{90}{15} \right)}^{2}}\] \[={{\left( \frac{6}{1} \right)}^{2}}\] \[=36:1\]
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