Question

A uniform rope of length l is pulled by a constant force F as shown. What is the tension in the rope at distance x form the end where the force is applied?

Answer 1

$a=\frac{F}{M}$

Mass per unit length $\lambda =\frac{M}{l}$

Hence mass of the part of length $(l-x)$ is given by $m=\lambda (l-x)$

$⟹m=\frac{M(l-x)}{l}$

For this part-

$T=ma=\frac{M(l-x)}{l}\times \frac{F}{M}$

$⟹T=\frac{F(l-x)}{l}$