A bead can slide on a smooth straight wire and a particle of mass m is attached to the bead by a light string of length L . The particle is held in contact with the wire with the string taut and is then let fall. The bead has mass 2m . When the string makes an angle `theta` with the wire the bead will have slipped a distance equal to

Options

A. `L(1 - cos theta)`
B. `((L)/(2)) (1 - cos theta)`
C. `((L)/(3)) (1 - cos theta)`
D. `((L)/(6)) (1 - cos theta)`

Answer

C

Explanation

Let `x =` displacement of ring to the left
`rArr Deltax_(cm) = (2mx + m(x + L - L cos theta))/(3m) = 0`
`rArr x = -(1)/(3) (1 - cos theta)`