question_answer

A string 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)  \[\frac{1}{2}F\]

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 :

 Force F is applied \[\therefore \] Acceleration in string\[=\frac{F}{M}\] \[m=\]mass of string mass per unit length of string \[=\frac{M}{L}\] Tension at a distance \[(l)\] \[=m\times a=mass\text{ }of\text{ }AB\times a\] \[\frac{m}{L}(L-l)\times \frac{F}{M}=\left( 1-\frac{1}{L} \right)F\]