Question

A uniform rope of length L resting on a smooth horizontal floor is pulled at one end by a force $l$. The tension in the rope at a distance L/4 from the end where the force is applied is then

• A. $F/4$
• B. $F$
• C. $4F/3$
• D. $3F/4$

Answer 1

The correct option is D $3F/4$

Linear mass density of rope $=\lambda$

Mass of rope M $=\lambda L$

$a=\frac{F}{\lambda L}$

Mass of that of the string $=\lambda (L-\frac{L}{4})$

$=\frac{3}{4}L\lambda$

$T=\lambda \left(\frac{3}{4}\right)La$
$=\frac{3}{4}\times L\frac{F}{\lambda L}=\frac{3F}{4}$