Question

A rope of mass $5kg$ is moving vertically with an upward force of $100N$ acting at the upper end and a downward force of $70N$ acting at the lower end. The tension at the midpoint of the rope is
(Take $g=10m/s^2$)

• A. $100N$
• B. $85N$
• C. $75N$
• D. $105N$

Answer 1

The correct option is B $85N$

FBD of the rope will be

Using FBD, we can write $70+5\times g-100=5\times a$ $⟹a=4m/s^2$
Hence rope will be accelerating downwards with an acceleration of $4m/s^2$
Let $T$ be the tension at the mid-point of the rope
Now, draw the FBD of upper half of this rope

Using FBD, we can write $T+2.5\times g-100=2.5\times a$ $⟹T=85N$