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 ?
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Options

A. The bodies will move together if `F = 0.25mg`
B. The body `A` will slip with respect to B if `F = 0.5mg`
C. The bodies will be at rest if `F = 0.5 mg`
D. The maximum value of `F` for which the two bodies will move together is `0.45 mg`

Answer

a,b,d,e

Explanation

Here, mass of `B = m`, mass of `A = (m)/(2)`
(a) Force of friction between `A` and `B f_(1) = 0.2 ((m)/(2)) g = 0.1 mg`
Force of friction between `B` and floor `f_(2) = 0.1 (m + (m)/(2)) g = (0.3)/(2) mg = 0.15mg`
The bodies will move together, if `F = f_(1) + f_(2) = 0.1 mg + 0.15mg = 0.25mg`
If `F= 0.5mg` force between `A` and `B` will exceed `0.1mg` and the the body A will slip
The bodies cannot move together when `F= 0.5mg`
If `F =0.1mg` the bodies will be at rest as `Flt(f_(1) + f_(2))`
The two bodies will move together till max accelerating force on `A = 0.1 mg = f_(1)`
acceleration of `A = (0.1mg)/(m//2) = 0.2g` acceleration of `B = 0.2 g`
max acc. force on `B = m xx 0.2g = 0.2 mg`
As `F_(2) =0.15mg`
`:.` Maximum value of `F` for with `A` and `B` will move together = `0.1 mg + 0.1 mg + 0.2 mg + 0.15mg = 0.45mg`
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