A plank of mass `2 kg` and length `1 m` is placed on horizontal floor.A small block of mass `1 kg` is placed on top of the plank , at its right extreme end .The coefficient of friction between plank and floor is `0.5` and that between plank and block is `0.2` . If a horizontal force `= 30 N` starts acting on the plank to the right ,the time after which the block will fall off the plank is `(g = 10 ms^(-2))`

Options

A. `((2)/(3)) s`
B. `1.5 s`
C. `0.75 s`
D. `((4)/(3)) s`

Answer

A

Explanation

`(f_(1))_(max)` = between `1 kg and 2 kg`

`= 0.2 xx 1 xx 10 = 2 N`
`(f_(2))_(max) = between 2 kg` and ground
`= 0.5 xx 3 xx 10 = 15 N`
`a_(1) = (2)/(1) = 2 m//s^(2)`
`a_(2) = (30 - 15 - 2)/(2)`
`= 6.5 m//s^(2)`
`a_(r) = a_(2) - a_(1)`
`4.5 = m//s^(2)`
`t = sqrt((2 S_(r))/(a_(r)))`
`= sqrt((2 xx 1)/(4.5)) = (2)/(3) s`