Question

An object of mass m is traveling around a circle of radius v. What happens to the centripetal force if the radius is cut in half?

Answer 1

Answer:

Centripetal force doubles

Explanation:

Since centripetal force is given by

$F=\frac {mv^{2}}{r}$

Where F is the centripetal force, m is the mass, v is the centripetal velocity and r is circle radius.

When the radius is reduced to half then the centripetal force will be

$F=\frac {mv^{2}}{0.5r}=\frac {2mv^{2}}{r}$

Evidently, the centripetal force is doubled compared to the initial.

Note that while the question gives letter v for radius, I used v for velocity and r for radius since these are the standard letters for abbreviating formula of centripetal force.