Here `f_(1) =` force of friction between man and plank `f_(2) =` force of friction between man and plank and surface
for the plank not to move
`F- (f_(2))_(max) le f_(1) le F + (f_(2))_(max)`
or `F - mu (M + m) g le ma le F + mu (M + m) g`
or a should lie between `(F)/(m) - (mu (M + m) g)/(m)`
and `(F)/(m) + (mu (M + m) g)/(m)`