A uniform rope of length 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.

Explanation

Let `M` be the mass of rope
Acceleration of rope `a=(F)/(M)`
Now we divide the rope into two parts by applying a cut at `P`

`T=(M)/(L)(L-x)a"
"F-T=(M)/(L)xa`
`=(M)/(L)(L-x)(F)/(M)" "=(M)/(L)x(F)/(M)`
`=F(1-(x)/(L))" "T=F(1-(x)/(L))`
We can find the tension at point `P` by taking either part.