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)

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, $R_2=2R_1$
$\therefore$ $\frac{F_2}{F_1}=\frac{R_1}{2R_1}=\frac{1}{2}$
or $F_2=\frac{F_1}{2}$
Therefore, centripetal force will become half.