A block of mass `2m` is attached to a string of length `L = 5 m`. The block is released when the string is horizontal , it picks up a particle of `2 m` kept at rest at the lowest point. The maximum height attached by the combined mass is

Options

A. `1 m`
B. `1.25 m`
C. `1.5 m`
D. `2.0 m`

Answer

B

Explanation

`v^(2) = 2 gL rArr v = sqrt(2 gL)`
`2 mv = ( 2m + 2m)v'`
`v' = (v)/(2) = sqrt((gL)/(2)) lt sqrt( 2 gL)`
`0 = v'^(2) - 2gh rArr (gL)/(2) = 2gh`
`h = (L)/(4) = (5)/(4) = 1.25 m`