Question

# A uniform rope of length $$L$$ is pulled by a force $$F$$ on a smooth surface. Find tension in the rope at a distance $$x$$ from the end where force is applied.

Solution

## Let the mass of the rope $$AB$$ be $$m$$ . Acceleration of the rope = $$a$$ = $$\dfrac{F}{m}$$Let the force be applied at the end A and the point at a distance $$x$$ from point $$A$$ be $$P$$ .Tension in the rope at a distance x from end $$A$$ (at point $$P$$)                    = Force required to move the remaining part with acceleration $$a$$Linear mass density of the rod = $$\dfrac{m}{l}$$Mass of the remaing part i.e. part $$PB$$ = $$\dfrac{m}{l}(l-x)$$Force required to move the remaining part = mass*acceleration                                                                         = $$\dfrac{m}{l}(l-x)$$$$\dfrac{F}{m}$$Therefore , tension in the rope at a distance $$x$$ from the end at which the force is applied is  $$F(\dfrac{l-x}{l})$$.Physics

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