Answer:
a) One-ninth the force acting on object A.
Explanation:
First, we derive an expression for the centripetal force acting on both objects.
For object A, centripetal force is:
[tex]F_A = \frac{m{v_A}^2}{r}[/tex]
For object B, centripetal force is:
[tex]F_B = \frac{m{v_B}^2}{r}[/tex]
We are given that they have the same mass and they move in circles of the same radius.
If object A completes three times as many rotations as object B, then, object must have 3 times the speed of object B.
Hence:
[tex]{v_A} = 3*{v_B}[/tex]
Therefore, [tex]F_A[/tex] becomes:
[tex]F_A = \frac{m({3*v_B}^{2} )}{r}\\\\\\F_A = \frac{9m{v_B}^{2}}{r}[/tex]
[tex]F_A = 9F_B[/tex]
=> [tex]F_B = \frac{1}{9} F_A[/tex]
Therefore, the net centripetal force acting on object B is one-ninth of the force acting on object A.
