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)

Mass of length $l=mL$, where $m$ is mass per unit length of the rope.

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