Question

A particle is suspended from a fixed point by a string of length $l$. It is projected from the equilibrium position with a velocity $v=2\sqrt{gl}$ as shown in the figure below, which of the following statements is true?

• A. The particle reaches point $\text{C}$ and undergoes free fall along the diameter $\text{CA}$
• B. The particle reaches a point between $\text{B}$ and $\text{C}$ where tension and velocity are both zero and free falls.
• C. The particle reaches a point between $\text{B}$ and $\text{C}$, where tension is zero but velocity is not zero, and follows a parabolic path
• D. The particle never reaches point $\text{B}$ and it oscillates between $\text{B}$ and $\text{C}$

Answer 1

The correct option is C The particle reaches a point between $\text{B}$ and $\text{C}$, where tension is zero but velocity is not zero, and follows a parabolic path

Given velocity of projection $v=\sqrt{4gl}$
Projection velocity is greater that $\sqrt{2gl}$ (minimum velocity required to reach point $\text{B}$)
and less than $\sqrt{5gl}$ (minimum velocity required to reach point $\text{C}$).
$\therefore$ Tension is zero somewhere between $\text{B}$ and $\text{C}$ where velocity $=0$
$\therefore$ It will leave the circular path between $\text{B}$ and $\text{C}$ and follow a parabolic path.