Question: A bead $\backslash ($ A $\backslash )$ weighing $9$ N with a hole in the center is able to slide on a quarter$-$circular frictionless bar $\backslash ($ B C $\backslash )$ with radius $\backslash ($ r $\backslash ).$ The bead is supported by a flexible but inextensible string $\backslash ($ A C $\backslash ).$ For the value of $\backslash (\backslash$theta$=20^\{\backslash$circ$\}\backslash )$ in the figure $($a$),$ compute the force supported by the string if the contact of the bead is shown in figure $($b$)$ where the size of the hole is bigger than the thickness of the bar.

$(20$ marks$)$

$($b$)$