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

Answer

B

Explanation

Horizontal acceleration of the system is
`a=(F)/(2m+m+2m)=(F)/(5m)`
Let `N` be the normal reaction between `B` and `C` . Free body diagram of `C` gives
`N=2ma=(2)/(5)F`
Now `B` will not slide downward if `muNgem_(B)g`
or `mu((2)/(5)F)gemg` or `Fge(5)/(2mu)mg`
or `F_(min)=(5)/(2mu)mg` .