A) twice as great as before
B) half
C) one-fourth
D) remains constant
Correct Answer: B
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.
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