Question

A fixed ring of mass m has two beads A, B of mass m each; both being able to slide on the ring without friction. Initially the ring lies on a frictionless horizontal table and the beads are given velocities ${\nu }_0$ , relative to the ring, in the same direction. The initial relative acceleration of one of the beads with respect to the other is

• A. $zero$
• B. $\frac{v_0^2}{R}$
• C. $\frac{2v_0^2}{R}$
• D. $\frac{v_0^2}{2R}$

Answer 1

The correct option is C $\frac{2v_0^2}{R}$

In their respective rest frames we have the centrifugal forces acting on the particles. Radially out ward,

Thus the relative acceleration is,
$a_{12}=a_1-a_2$
$=\frac{V_0^2}{R}-(-\frac{V_0^2}{R})$
$=\frac{2V_0^2}{R}$