Question

An object is moving in a circular path with a constant velocity (v). If the radius of the circle in which the object is moving is decreased by one half and the velocity remains the same, what will happen to the centripetal force?

• A. It will be $4F$
• B. It will be $2F$
• C. It will be F
• D. It will be $F/2$
• E. It will be $F/4$

Answer 1

The correct option is B It will be $2F$

Initial centripetal force $F=m{v}^2/r$

Now the radius is decreased by one half , so new radius $r^{\prime }=r/2$

and new centripetal force $F^{\prime }=m{v}^2/r^{\prime }=\frac{m{v}^2}{\frac{r}{2}}$

or $F^{\prime }=2m{v}^2/r=2F$