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. `u=sqrt((gl)/5)`
B. `u=sqrt((8gl)/5)`
C. `v=sqrt(3gl)`
D. `v=sqrt((3gl)/5)`

Answer

A, D

Explanation

`vcostheta=usintheta`
From conservation of energy
`mglcostheta=2(1/2"mu"^(2))+1/2mv^(2)`
`u=sqrt((2glcostheta)/(2+tan^(2)theta)) =sqrt((gl)/5)` using `theta=60^(@)`
`v=sqrt((3gl)/5)`