Question

Two painters are working from a wooden board $5$ 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 $x$ m from the centre of mass of the board on the other side. Take mass of the board as 20 kg and $g=10m{s}^{-2}$. The range of $x$ so that both the painters can work safely is :

• A. $\frac{1}{3}<x<\frac{11}{6}$
• B. $0<x<\frac{11}{6}$
• C. $0<x<\frac{10}{3}$
• D. $\frac{1}{3}<x<2$

Answer 1

Answer: (C)

$0<x<\frac{10}{3}$

For vertical equilibrium, $T_1+T_2=1600N$...(i)

Take moment about O,

$T_1\times 2.5+600x-T_2\times 2.5\times 1-800\times 1$....(ii)

$T_1+240x-T_2-320=0$....(iii)

Solving equations (i) and (iii)

$T_1=960-120x$

and $T_2=640+120x$

For safe working, $T_1<1040$ and $T_2<1040N$

$x>0$ and $x<\frac{10}{3}$, so the range is $0<x<\frac{10}{3}$.