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 ${}^{\prime }{l}^{\prime }$ 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 = $\frac{M}{L}$

$Ma=F\Rightarrow \lambda La=F\Rightarrow a=\frac{F}{\lambda L}$

$T=ma=\lambda (L-l)a$

$T=\lambda (L-l)\frac{F}{\lambda L}=(1-\frac{l}{L})F$