Question

A rope of length $l$ is pulled with a constant force $f$. $T$ is the tension in the rope at a point distant $x$ from the end where the force is applied. Then $T$ is:

• A. $f(l-x)/l$
• B. $fl/(l-x)$
• C. $\frac{(f-x)}{l-x}$
• D. $\frac{fl}{x}$

Answer 1

The correct option is A $f(l-x)/l$

Let $m$ be the mass per unit length of the rope.

for part PB, $f-T=mxa.....\left(1\right)$

for part PA, $T=m(l-x)a...\left(2\right)$

$\left(1\right)+\left(2\right),f=mxa+mla-mxa=mla\Rightarrow a=\frac{f}{ml}$

now using (2), $T=m(l-x).\frac{f}{ml}=\frac{(l-x)f}{l}$