Question

A $14{\text{kg}}$ block is hanged using a system of pulleys as shown in the figure. Tension in the string connecting the ceiling and topmost pulley is

A. $17.5{\text{N}}$
B. ${\text{70N}}$
C. $140{\text{N}}$
D. ${\text{280N}}$

Answer 1

The given question is based on pulleys which are associated with tension in the string due to a block hanging from it. We need to apply Newton’s second law of motion which defines the force due to a mass to each pulley separately and equates it with the tension in the string.

Complete step by step answer:
We know that the pulleys connected have a tension in each of their strings which is divided among the pulleys depending on the position of the pulley. In this problem, we need to find the tension in the uppermost pulley connected to the ceiling but for that, we have to know the tensions in each of the pulleys below it.

Let us first draw the free body diagram of the system and label the tensions in each string.We know that the tension in both the strings of the pulley is the same for the same pulley.

As we can see from the diagram, the topmost pulley is experiencing tension $8{\text{T}}$ due to the pulleys and the block below it. We will assume that the system is in equilibrium and equate the tension and weight of the block.
$8{\text{T = mg}}$
Where $m$ is the mass of the block hanging and $g$ is the acceleration due to gravity.
Substituting the value of the mass we get
$8{\text{T = 14}} \times {\text{10}}$
$\therefore 8{\text{T = 140N}}$

Therefore the correct option is C.

Note: The question has asked for the tension in the topmost pulley attached to the ceiling and therefore we have not divided the answer by $8$ . We should also note that the tensions in the different pulleys in a system can be added and the net tension can be calculated. To solve such problems we assume that the system is in equilibrium because then only we can equate the upward and downward force.