In a figure shown mass of `A` and `B` is equal to `M` each. Friction between `B` and lowermost surface is negligible. Initially both the blocks are at rest. The dimensions of the block `A` are very small. A constant horizontal force `F` is applied on the blocks `B` and both the blocks start moving together without any relative motion. Suddenly, the block `B` encounters a fixed obstacle and comes to rest. The block `A` continues to slide on the block `B`. The block `A` just manages to reach the opposite end of the bolck `B`. What is the coefficient of friction between the two blocks? (Required length are shown in figure)

Options

A. `F/Mg`
B. `2F/ Mg`
C. `F/2Mg`
D. none of these

Answer

A

Explanation

Velocity of upper block when lower block hits an obstacle,
`v=sqrt(2al)=sqrt(2F/(2M)l)=sqrt((Fl)/M)`
Now after collision retardation of upper block wr.t earth.
`a=("mu"Mg)/M="mu"g`
`:. v^(2)=u^(2)+2as`
`0=(Fl)/(M-2"mu"gl/2implies"mu"=F/(Mg)`