Question

A uniform thick rope of length $10m$ and mass $10kg$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $20N$ from one end. The tension in the rope at $2m$ from the end where the force is applied is,

• A. $4N$
• B. $8N$
• C. $16N$
• D. $20N$

Answer 1

Answer: (C)

The acceleration of the rope, $a=\frac{F}{m}=\frac{20}{10}=2m{s}^{-2}$ .
The mass of the remaining portion of the $8m$ rope pulled by tension,
$m_2=\frac{M}{L}{l}_2=\frac{10}{10}\times 8=8kg$ .
Tension in the rope at $2m$ from the end where force is applied,
$T=m_{2}a$
$\Rightarrow T=8\times 2=16N$ .