A ball `A` of mass `m` attached to a string of length `L` is released when the string is horizontal. It strikes another ball `B` of mass `2 m` suspended to another string of length `L` at rest as shown. Find the maximum angle made by the string if the collision is completely inelastic.

Explanation

when ball `A` reaches to ball `B` , its velocity
`u = sqrt( 2 gL)`
By the momentum conservation
`m sqrt( 2 gL) + 2 m xx 0 = ( m + 2m) V rArr V = (1)/(3) sqrt( 2 gL)`
Since `V prop sqrt(2 gL)` , the combined mass will oscillate like a simple pendulum , hence , the maximum angle made by the string with vertical `lt 90^(@)`.
`0 = V^(2) - 2gh`
` 0 = (1)/(9) 2 gL - 2gL ( 1 - cos theta)`
`1 - cos theta = (1)/(9) rArr cos theta = (8)/(9) rArr theta = cos6(-1) ((8)/(9))`