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  4. A particle is moving in a circle of radius R with constant speed v. If radius is doubled, then its centripetal force to keep the same speed gets:

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Q. A particle is moving in a circle of radius R with constant speed v. If radius is doubled, then its centripetal force to keep the same speed gets:

Bihar CECEBihar CECE 2005Motion in a Plane

Solution:

Centripetal force is given by
$ F=\frac{m{{v}^{2}}}{R} $
where m is mass of particle, $ v $ is speed, and R is radius of circular path.
$ \Rightarrow $ $ F\propto \frac{1}{R} $
or $ \frac{{{F}_{2}}}{{{F}_{1}}}=\frac{{{R}_{1}}}{{{R}_{2}}} $
Given, $ {{R}_{2}}=2{{R}_{1}} $
$ \therefore $ $ \frac{{{F}_{2}}}{{{F}_{1}}}=\frac{{{R}_{1}}}{2{{R}_{1}}}=\frac{1}{2} $
or $ {{F}_{2}}=\frac{{{F}_{1}}}{2} $
Therefore, centripetal force will become half.