A system is pushed by a force `F` as shown in figure All surfaces are smooth except between `B` and `C` is `mu`. Minimum value fo `F` to prevent block `B` from down ward slipping is

Options

A. `((5)/(3 mu)) mg`
B. `((5)/(2 mu)) mg`
C. `((5)/(2))mu mg`
D. None of these

Answer

a

Explanation

a.Common acceleration , `a = (F)/(5m)`
Taking A and B togather as system.
`N = (2m + m)(F)/(5m) = (3)/(5)F`

FBD of blockB
block B is sliding `f = mg and f le muN`
`mg le mu (3)/(5)F rArr F ge (5mg)/(3mu)`