Two small rings, each of mass `'m'`, are connected to the block of same mass `'m'` through an inextensible massless string of length `'l'`. Rings are constrained to move over smooth rod `AB`. Initially, the system is held at rest as shown in Fig. Let a and `v` be the velocities of ring and block, respectively when string makes an angle `60^(@)` with the vertical.

Options

A. `sqrt((3gl)/(5))`
B. `sqrt((gl)/(5))`
C. `sqrt((5gl)/(4))`
D. None of these

Answer

A

Explanation

`v cos theta = u sin theta`
`v = sqrt(3)u`…….(i)
`mg l costheta = "mu"^(2) + v`……(ii)

`u = sqrt((gl)/(5)),v=sqrt((3gl)/(5))`