Question

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. The net centripetal force acting on object B is... a) ...one-ninth the force acting on object A. b) ...one-third the force acting on object A. c) ...three times the force acting on object A. d) ...nine times the force acting on object A. e) ...the same as the force acting on object A. Explain your choice in the space provided.

Answer 1

The net centripetal force acting on object B is one-ninth of the force acting on object A.

Step-by-step explanation:

The centripetal force acting on an object when movieng in circular paath is given by :

`F=mr\omega^2`

Here,

m is the mass of the object

r is the radisu of circular path

`\omega` 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 :

`(F_A)/(F_B)=((\omega_A)/(\omega_B))^2\\\\(F_A)/(F_B)=((3\omega_B)/(\omega_B))^2\\\\(F_A)/(F_B)=9\\\\(F_B)/(F_A)=(1)/(9)\\\\F_B=(F_A)/(9)`

So, the net centripetal force acting on object B is one-ninth of the force acting on object A.