Question

The pull $\mathrm{P}$ is just sufficient to keep the block of weight $14\mathrm{N}$ in equilibrium as shown. Pulleys are ideal. Find the value of $\mathrm{P}$.

• A. $4\mathrm{N}$
• B. $6\mathrm{N}$
• C. $8\mathrm{N}$
• D. $2\mathrm{N}$

Answer 1

The correct option is D

$2\mathrm{N}$

Step 1: Given parameters

Tension is the pulling force that acts on the body as it is suspended from objects such as chains, cables, and strings. It is denoted by $T$.

Let $T_1,T_2,T_3,$ and $T_4$ are tensions in the cables.

We know that tension is simply the pull on the cable

Now,

$$\begin{gathered} T_1=\mathrm{P} \\ {T}_2=2T_1=2\mathrm{P} \\ {T}_3=2T_2=4\mathrm{P} \\ {T}_4=2T_3=8\mathrm{P} \end{gathered}$$

Step 2: Calculation

As the upper cable is connected to the ceiling, the tension on the pulley $\left(T_4\right)$ is taken up by the cable. Hence, the $T_4$ is neglected from the calculation.

Applying equilibrium conditions to block,

$T_1+T_2+T_3=14\mathrm{N}...\left(1\right)$

Substitute values of $T_1,T_2,T_3$ in equation (1).

$$\begin{gathered} \mathrm{P}+2\mathrm{P}+4\mathrm{P}=14\mathrm{N} \\ 7\mathrm{P}=14\mathrm{N} \\ \mathrm{P}=2\mathrm{N} \end{gathered}$$

Hence, option (D) is correct.