Initially the blocks are at rest with `F=0`. `F` is gradually increased.

From `F=0` till `F=F_(1)`, no motion
From `F gt F_(1)` till `F=2F_(1)`, motion with relative acceleration `=0`
From ` F gt 2F_(1)`, relative acceleration non-zero
At `F=3F_(1)`, relative acceleration `= 2 ms ^(-2)`
Then,

Options

A. `m=2 Kg`
B. `mu_(1)=0.4`
C. `F_(1)=6N`
D. At `F=4F_(1)`, relative acceleration is `4 ms^(-2)`

Answer

A, D

Explanation

System starts accelerating when `F=F_(1)`
`F_(1)=0.1 (m+2)g`…(i)
`F_(1)leF le2F_(1)` no relative acceleration, a is common accceleration when `F=2F_(1)`
`2F_(1)-mu_(1)2g=2a….(ii)2F_(1)-mu_(1)2g=2a..(iii)`
`F=3F_(1)` relative acceleration is `2 m//sec^(2)`
`(3F_(1)-mu_(1)2g)/(2)-a=2`...(iv) solving equations
`F_(1)=4,m=2,a=1,mu=0.3`
`F=4F_(1)` relative acceleration is `(4F_(1)-mu_(1)2g)/(2)-a`
putting values relative acceleration is `4 ms^(-2)`