Both the blocks are given same velocity towards right. In how much time , the smaller block will separate from the large block.

Explanation

Upper block :
`uarr : N_(1) - mg = 0`
`rArr N_(1) = mg`
`f_(1) = mu_(1) N_(1) = (1)/(2) xx mg = (mg)/(2)`
Retardation `a_(1) = (f_(1))/(m) = (g)/(2)`
Lower block :
`uarr : N_(2) - ( 4m + m) g = 0`
`rArr N_(2) = 5 mg`
`f_(2) = mu_(2) N_(2) = 1 xx 5 mg = 5 mg`
Retardation `a_(2) = (f_(2) - f_(1))/(4m) = (5 mg - (mg)/(2))/(4 m) = (9 g)/(8)`
`a_(2) gt a_(1)` , i.e. the upper block is accelerating w.r.t. the lower block.
Acceleration of the upper block with respect to the lower block
`a_(1//2) = a_(2) - a_(1) = (9 g)/(8) - (g)/(2) = (5g)/(8)`
Relative velocity `v_(1//2) = 0`
`s = (1)/(@) a_(1//2) t^(2)`
`0.5 = (1)/(2) (5g)/(8) t^(2) = (50)/(16) t^(2)`
`t^(2) = 0.16 rArr t = 0.4 s`