Question

In the figure, the force with which the man should pull the rope to hold the plank in position is $F$. If weight of the man is $60kg$, the plank and pulleys have negligible masses, then $(g=10m/s^2)$:

• A. $F=15kgf$
• B. $F=30kgf$
• C. $F=60kgf$
• D. $F=120kgf$

Answer 1

The correct option is A $F=15kgf$

The conditions of equilibrium

$Fnet=0$

Man on the plank as a system

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

For plank as a system

$3T-N=0$ ....($2$)

Substitute $T$ from eq$1$ in eq$2$

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

$3mg=4N$

$3/4mg=N$

now substitute $N$ in eq$1$

$T=mg-3/4mg$

Mag of weight $=60$

$T=60-45$
$T=15$

Thus force applied is $15kgf$