Two painters are working from a wooden hoard `5 m` long suspended from the top of a building by two ropes attached to the ends of the plank. Either rope can withstand a maximum tension of `1040 N`. Painter `A` of mass `80 kg` is working at a distance of `1 m` from one end. Painter `B` of mass `60 kg` is working at a distance of `x` in from the centre of mass of the board on the other side. Take mass of the board as `20 kg` and `g = 10ms^(-2)`. The range of `x` so that both the painters can work safely is

Options

A. `1/3ltxlt11/6`
B. `0ltxlt11/6`
C. `0ltxlt2`
D. `1/3ltxlt2`

Answer

C

Explanation

For vertical equilibrium `T_(1)+T_(2)=1600N`

Take momnet about `O`
`T_(1)xx2.5+600x`
`T_(2)xx2.5+800xx1.5`
`T_(1)=1040-120x`
and `T_(2)=560+120x`
For safe working `T_(1)lt1040 N` and `T_(2)lt1040Nxgt0` and `xlt2`, so the range is `0ltxlt2.`