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 ?

A uniform rope of length L rests on a smooth plane. One end of the rop

1.	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 ?
Answer» SOLUTION :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 accelerationa 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)`.