question_answer

A uniform rope of length L, resting on a frictionless horizontal surface, is pulled at one end by a force F. The tension in the rope at a distance I from this end is

A) \[F\]                                     

B) \[\frac{l}{L}F\]

C) \[\frac{L}{l}F\]                                  

D) \[\left( 1-\frac{l}{L} \right)F\]

Correct Answer: D

Solution :

Mass of length\[l=mL\], where m is mass per unit length of the rope. From Newtons 2nd law, \[Force=mass\times acceleration\]                 \[F=mL\,\,a\] \[\Rightarrow \]               \[a=\frac{F}{mL}\] Tension in rope at distance I from the given end                 \[T=m(L-l)a\]                 \[=m(L-l)\frac{F}{mL}\]                 \[T=\left( 1-\frac{l}{L} \right)F\]