Question

With what force must a man pull on a rope to hold a plank in position if the man weights $60kg,$ neglecting the weight of the plank$,$ rope and pulley$?$

• A. $15$ kg wt
• B. $90$ kg wt
• C. $40$ kg wt
• D. $180$ kg wt

Answer 1

The correct option is A $15$ kg wt

The conditions of equilibrium$:$

$F_{net}=0$

Man on the plank as a system

$T+N-mg=0$................................$\left(1\right)$

For plank as a system

$3T-N=0$ ....................$\left(2\right)$

Substituting $T$ from $e{q}^n\left(1\right)$ in $e{q}^n\left(2\right)$

we get $3mg-3N-N=0$

$3mg=4N$

$3/4mg=N$

Now$,$ substitute N in $e{q}^n\left(1\right)$

$T=mg-3/4mg$

Mag of Weight $=60$

$T=60-45$

$T=15$

Thus force applied is $15kgwt$

hence,

option $\left(A\right)$ is correct answer.