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
A) twice as great as before
B) half
C) one-fourth
D) remains constant
Explanation
(b) Centripetal force is given by
$F = \frac{{mv}^{2}}{R}$
$\Longrightarrow F \propto \frac{1}{R}$
$or\frac{F_{2}}{F_{1}} = \frac{R_{1}}{R_{2}}$
$Given,\ \ r_{2} = 2r_{1}$
$\therefore\frac{F_{2}}{F_{1}} = \frac{R_{1}}{{2R}_{1}} = \frac{1}{2}$
$or\ \ F_{2} = \frac{F_{1}}{2}$
therefore, centripetal force will become half.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.