Question

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:

• A. twice as great as before
• B. half
• C. one-fourth
• D. remains constant

Answer 1

Answer: (B)

half

Answer 2

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.