question_answer

A spring of length L and uniform cross-section is spread on a smooth plane. One of its ends is pulled by a force F. Find the tension in it at a distance I from this end.

A)  \[\frac{l}{2}F\]                                 

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

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

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

Correct Answer: C

Solution :

Mass per unit length of string  \[=\frac{M}{L}\]acceleration in string due to force F                 \[a=\frac{F}{M}\]                 Tension at a distance ( from end (Q) is T = force on part PO                       = mass of part \[PO\times \]acceleration or        \[T=\frac{M}{L}(L-l)\times \frac{F}{M}\] \[\Rightarrow \]               \[T=\left( 1-\frac{l}{L} \right)F\]