Two beads A and B move along a semicircular wire frame as shown. The beads are connected by an inelastic string which always remains tight. At an instant the speed of A is $u$ . $\angle BAC=45^{\circ}$ and angle $BOC=75 ^{\circ}$ where O is center of the semicircular arc. The speed of bead B at that instant is

Question

$$(a)\;\sqrt 2 u \quad (b)\; u \quad (c)\;\frac{u}{2 \sqrt 2} \quad(d)\;\sqrt {\frac{2}{3}}u$$