A uniform rope of length L rests on a smooth plane. One end of the rope is pulled with a force F. what is the tension in the rope at a distance l from that end ?

Explanation

Let the mass of the rope be M
Hance, mass per unit length of the uniform rope = `(M)/(L)`.
Length of the part BC of the rope = l .
length of the part AC = L - l,
and mass of the part AC = `(M)/(L)` (L - l) .
Acceleration of the rope due to the force F is a = `(F)/(M)`.
Let the tension at C be T.
Hence, part AC of the rope gains acceleration a due to the tension T.
`therefore` T = mass of AC `xx` acceleration of the rope
` = (M)/(L) (L - l)cdot (F)/(M) = (F)/(L) (L-l)`.