Question

In the given diagram, with what force must be man pull the rope to hold the plank in position? Weight of the man is $60kg$. Neglect the weights of plank, rope and pulley :

• A. $15kgf$
• B. $20kgf$
• C. $25kgf$
• D. $30kgf$

Answer 1

The correct option is A $15kgf$

$\text{Step 1: Free body diagram}$ $\text{[Ref. Fig.1]}$

From FBD of man

$T+N_o=mg$ $.........\left(1\right)$

From FBD of plank

$2T+T-N_0=0$

$3T-N_0=0$ $..........\left(2\right)$

$\text{Step 2: Solving equation}$

For man to hold the Plank in this position, net force on it should be zero.

$F_{net}=0$

Substitute value of $T$ from equation $\left(1\right)$ in $\left(2\right)$

$3(mg-N_0)-N_o=0$

$\Rightarrow N_o=\frac{3}{4}mg$

From equation $1$

$T+\frac{3}{4}mg=mg$

$\Rightarrow$ $T=\frac{1}{4}mg=\frac{1}{4}\left(60\right)kgf$ $=15kgf$

Hence, option $A$ is correct.

$\text{Alternate Solution-}$ $\text{[Ref. Fig.2]}$

Consider both plank and man as a system

For system (Plank+Man) $F_{net}=0$

From FBD

$2T+T+T=mg$

$T=\frac{1}{4}mg=\frac{1}{4}\times 60kgf$

$=15kgf$