Question

A straight rope of length 'L' is kept on a frictionless horizontal surface and a force 'F' is applied to one end of the rope in the direction of its length and away from that end. The tension in the rope at a distance 'l' from that end is

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

Answer 1

The correct option is C $(1-\frac{l}{L})F$


Let mass of the rope =M, and linear density =$\frac{M}{L}$
$Ma=F\Rightarrow \lambda La=F\Rightarrow a=\frac{F}{\lambda L}$
$T=ma=\lambda (L-l)a$
$T=\lambda (L-l)\frac{F}{\lambda L}=(1-\frac{l}{L})F$