question_answer

A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance y from the end at which the force applied is:

A) \[Zero\]                         

B) \[F\]

C) \[\frac{F\,(L-Y)}{L}\]                 

D) \[\frac{F\,(L-Y)}{M}\]

Correct Answer: C

Solution :

[c]                         \[a=\frac{F}{M}\]             \[F-T=\frac{M}{L}ya\]              \[F-T=\frac{M}{L}y\frac{F}{M}\]             \[F-T=F\frac{Y}{L}\]             \[T=F-\frac{Fy}{L}\]             \[T=F\,\left[ 1\frac{y}{L} \right]=T=F\left[ \frac{L-y}{L} \right]\]             In Rod \[L\,(m)\to M\]             \[I\,(m)\to \frac{M}{L}\]             \[(L-y)m\to \frac{M}{L}[L-y]\]                         \[y\,(m)\to \frac{M}{L}y\]