Question

A uniform rope of length $L$, resting on a frictionless horizontal surface, is pulled at one end by a force $F$. The tension in the rope at a distance $I$ from this end is

• A. $F$
• B. $\frac{l}{L}F$
• C. $\frac{L}{l}F$
• D. $\left( 1-\frac{l}{L} \right)F$

Answer 1

Answer: (D)

$\left( 1-\frac{l}{L} \right)F$

Answer 2

Mass of length $l=m L$, where $m$ is mass per unit length of the rope. From Newton's 2 nd law, Force $=$ mass $\times$ acceleration $F=m L a$ $\Rightarrow a=\frac{F}{m L}$ Tension in rope at distance $l$ from the given end $T =m(L-l) a$ $=m(L-l) \frac{F}{m L}$ $T=\left(1-\frac{l}{L}\right) F$