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

`a_(1//g)=2 m//s^(2)`
`a_(2//g)=(30-2-15)/(2)=(13)/(2)=6.5m//s^(2)rArra_(2n)=4.5`

`s_(2//1)=(1)/(2)a_(2//1)t^(2
)rArrt=(1)/(2)xx4.5xxt^(2)`
`rArrt=sqrt(4/9)=(2)/(3)` sec