A) \[\frac{{{r}_{1}}}{{{r}_{2}}}\]
B) \[\frac{{{r}_{2}}}{{{r}_{3}}}\]
C) \[\sqrt{\frac{{{r}_{2}}}{{{r}_{1}}}}\]
D) \[{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{2}}\]
Correct Answer: A
Solution :
Key Idea: For circular motion to occur centripetal force is a necessity. A body performing circular motion is acted upon by a force which is always directed towards the centre of the circle, this force is called centripetal force. \[F=\frac{m{{v}^{2}}}{r}\]where, m is mass, v is velocity and r is radius. Also, \[v=r\omega \] where, \[\omega \]is angular velocity. \[\therefore \] \[F=mr{{\omega }^{2}}\] Given, angular velocity is same, hence \[\Rightarrow \] \[\frac{{{F}_{1}}}{{{F}_{2}}}=\frac{{{r}_{1}}}{{{r}_{2}}}\]
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