Question

A uniform rope of mass $M$ and length $L$ is pulled along a frictionless inclined plane of angle $\theta$ by applying a force $F (> Mg )$ parallel to incline. Tension in the chain at a distance $x$ from the end at which force is applied is

• A. $F \frac{ x }{ L }+\frac{ x }{ L } Mg \sin \theta$
• B. $F \left(1-\frac{ x }{ L }\right)$
• C. $F \left(1-\frac{ x }{ L }\right)+\frac{ x }{ L } Mg \sin \theta$
• D. None of these

Answer 1

Answer: (B)

$F-M g \sin \theta=M a \dots$(1)
$F-\left(\frac{M}{L} x\right) g \sin \theta-T=\left(\frac{M}{L} x\right)$ a
$F-\left(\frac{M}{L} x g \sin \theta\right)-T=\frac{M}{L} x\left(\frac{F-M g \sin \theta}{M}\right)$
$T=F\left(1-\frac{x}{L}\right)$