In the co-efficinet of friction between the floor and the body `B` is 0.1. The co-efficient of friction beteen the bodies `B` and `A` is 0.2 A fore `F` is applied as shown `B` The mass of `A` is `m//2` and of `B` is m Which of the following statements are ture ?
.

Options

A. The bodies will move together if F = `0.25` mg .
B. The body A will slip with respect to B if F = `0.5` mg
C. The bodies will move together if F = 0.5 mg .
D. The bodies will be rest if F = 0.1 mg.

Answer

A, B, D

Explanation

`a_(c) = ((F)/(m + (m)/(2)))`

`f_(L) = ((2)/(10) xx (mg)/(2))`
`F_("required")` to have common acceleration
`F_(R) = ((m)/(2) xx a_(c))`
If `F_(R) le f_(L)`
Then they will have common acceleration .
If `F_(R) gt f_(L)` then they will have different acceleration .