Answer:
Option A: F/4
Explanation:
Centripetal force, [tex]F = \frac{mv^{2} }{r}[/tex]
Where v = speed
r = radius
Since Kinetic Energy, [tex]E_{k} = 0.5 mv^{2}[/tex]
Writing centripetal force in terms of kinetic energy, [tex]F = \frac{2 E_k}{r}[/tex]
If the initial radius of the circle, r₁ =r
The doubled radius, r₂ = 2r
If the initial kinetic energy, [tex]KE_1 = E_{k}[/tex]
The halved kinetic energy, [tex]KE_2 = 0.5E_{k}[/tex]
Therefore, the new Centripetal force becomes:
[tex]F_{2} = \frac{2(0.5 E_k)}{2r} \\F_{2} = \frac{0.5 E_k}{r}\\F_{2} =\frac{1}{4} * \frac{2 E_k}{r}\\Since, F = \frac{2 E_k}{r} \\F_{2} =\frac{1}{4} * F\\F_{2} =\frac{F}{4}[/tex]
