Two identical blocks `A` and `B` are placed on a rough inclined plane of inclination `45^(@)`. The coefficient of friction between block `A` and incline is `0.2` and that of between `B` and incline is `0.3`. The initial separation between the two blocks is `sqrt(2)m`. The two blocks are released from rest, then find the time (in sec) after which front faces of both blocks come in same line.

Explanation

From, `mg sin theta-muN=ma`, where `N=mg costheta`
`a_(A)=g sin 45^(@)-0.2g cos 45^(@)=4sqrt(2)m//s^(2)`
`a_(B)=g sin 45^(@)-0.3g cos 45^(@) =(7)/(2) sqrt(2)m//s^(2)`

Relative acceleration
`a_(AB)=0.5sqrt(2) m//s^(2)`
Relative displacement
`s_(AB)=(1)/(2)a_(AB)t^(2)=sqrt(2)` (given)
`t^(2)=(2sqrt(2))/(0.5sqrt(2))=4 rArr t = 2 sec.`
`s_(AB)=(1)/(2)a_(B)t^(2)=7sqrt(2)m`
`s_(A)=(1)/(2)a_(A)t^(2)=8sqrt(2)m`