# Velocity of bead when a light inextensible frictionless cord becomes taut. (Pathfinder methods of impulse build up 3rd question)

The complete question is

"A thin light inextensible frictionless chord of length $$l$$ wearing a small bead is tied between two nails that are in the same level a distance $$(0.5)l$$ apart. Initially the bead is held close to a nail and released. Find speed of the bead immediately after the chord becomes taut."

The Answer given is $$\sqrt{\frac{3gl}{20}}$$.

I tried to find $$h$$ by applying conditions for $$F_x=0$$ and pythagoras relation of $$x\ y$$ and $$h$$($$x$$ = part of rope on the side from which bead was released, $$y$$ = horizontal distance from the initial nail and $$h$$ = height it descended)

• I wouldn't trust a physics book whose author doesn't know what the word "chord" means... Commented Oct 1, 2023 at 12:26

## 2 Answers

Take the velocity to be perpendicular to net tension at the bottom point.Use pythagoras to find the angles.Try to solve Further

If the mass of the cord is ignored, then the bead will drop straight down (a distance h) until the cord is taunt. Then $$h^2 + (0.5L)^2 = (L – h)^2$$. I do not agree with the given answer.

• Yes I thought that too and did that too but I saw the answer was wrong so I thought my method was wrong. Its just that answer key of pathfinder though not entirely flawless but it is usually correct and we wrong. so I assumed it moved horizontally as well but that's where i got stuck. Thanks for your answer Commented Oct 17, 2021 at 9:18
• The bead cannot move horizontally until after the cord is taunt. Commented Oct 17, 2021 at 13:32
• I know right but the answer made me confused Commented Oct 17, 2021 at 14:18