Three blocks `A,B` and `C` of mass `m,m/2` and `m` of different densilties and dimensions are placed over each other as shown in the figure. The cofficients of friction are shown. Blocks placed in a vertical line are mae to over towards right with same velcity at the same instant. Find the time (in sec) taken by the upper block `A` to topple from the middle blcok `B`. Assume that blocks `B` and `C` don't stop sliding before `A` topples from `B`. (given `L=36m,mu=0.4` and `g=10 m//s^(2)`)

Answer

3

Explanation

Since `(mu)/4lt(mu)/4ltmu`, the upper block will move faster than the middle block and hence force of friction on upper block is towards left
`:.f=(mu)/4mg`
`:.a_(A)=(mug)/4` leftward

`f^(')=(mu)/2(m+m/2)g=3/4mumg`
`:.a_(B)=mug` (leftward) ltbgt `:.a_(A//B)=3/4 mug` (rightward)
For sliding down the block `B, A` has to move a distance `(3L)/8`
relative to block `B`.
`(3L)/8= 1/2 3/4 mu"gt"^(2)`
`:.t=sqrt(l/(mug))=3` sec