The block each of mass `1 kg` are placed as shown .They are connected by a string which passes over a smooth (massless) pulley.

There is no friction between `m_(1)` and the ground.The coefficient of friction between `m_(1)` and`m_(2)` is `0.2 A` force `F` is applied to `m_(2)`. Which of the fpllowing statement is/are correct?

Options

A. The system will be in equilibrium if `F le 4 N`
B. `F ge 4 N` tension in the string will be `4 N`
C. `F ge 4 N` the frictional force between the blocks will be `2 N`
D. `F = 6 N` tension in the string will be `3 N`

Answer

A, C, D

Explanation

Maximum value of friction between two blocks

`f_(max) = 0.2 xx 1 xx 10 = 2 N`
In critical case ,
`T = 2 N`
`F = T + 2 = 4 N`
`:.` System is in equation if `f le 4 N`
For `F gt 4 N`
`F - (T + 2) = m_(2)a = (1) (a)` ...(i)
`T - 2 = m_(2)a = (1) (a)` ...(ii)

On solving two equations, we get
`T = (F)/(2)`
when `F = 6 N, T = 3 N`