Answer :
Answer:
The net centripetal force acting on object B is one-ninth of the force acting on object A.
Explanation:
The centripetal force acting on an object when movieng in circular paath is given by :
[tex]F=mr\omega^2[/tex]
Here,
m is the mass of the object
r is the radisu of circular path
[tex]\omega[/tex] is angular velocity
Here, two identical objects (A, B) travel circles of the same radius but object A completes three times as many rotations as object B in the same time.
It is clear that, centripetal force is directly proportional to the square of agular velocity. New centripetal force becomes :
[tex]\dfrac{F_A}{F_B}=(\dfrac{\omega_A}{\omega_B})^2\\\\\dfrac{F_A}{F_B}=(\dfrac{3\omega_B}{\omega_B})^2\\\\\dfrac{F_A}{F_B}=9\\\\\dfrac{F_B}{F_A}=\dfrac{1}{9}\\\\F_B=\dfrac{F_A}{9}[/tex]
So, the net centripetal force acting on object B is one-ninth of the force acting on object A.