Two objects are traveling around different circular orbits with constant speed.They both have the same acceleration but object A is traveling twice as fast as object B.The orbit radius for object A is _______ the orbit radius for object B.
A)one-fourth
B)one-half
C)the same as
D)twice
E)four times

Question

Quizplus · Accepted Answer

The centripetal acceleration formula is $a = \frac{v^2}{r}$, where $a$ is the acceleration, $v$ is the velocity, and $r$ is the radius of the circular path. Given that both objects have the same acceleration but object A is traveling twice as fast as object B ($v_A = 2v_B$), we can set their accelerations equal to each other: $\frac{(2v_B)^2}{r_A} = \frac{v_B^2}{r_B}$. Simplifying gives $\frac{4v_B^2}{r_A} = \frac{v_B^2}{r_B}$, which further simplifies to $r_A = 4r_B$. Thus, the orbit radius for object A is four times the orbit radius for object B.

Two Objects Are Traveling Around Different Circular Orbits with Constant