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. `((3)/(2 mu))mg`
B. `((5)/(2 mu))mg`
C. `((5)/(2)) mu mg`
D. `((3)/(2)) mu mg`

Answer

B

Explanation

Horizontal acceleration of the system is

`a = (F)/(2m _ m + 2m) = (F)/(5m)`
Let `N` be in the normal reaction between B and C free body diagram of C given
`N = 2ma= (2)/(5) F`
Now B will not slide downwards if `mu N 2m_(B)g`
`or mu((2)/(5)F) 2 mg or F ge (5)/(2a) mg`
`so F_(max) = (5)/(2a) mg`