Question

Two beads $A$ and $B$ move along a semicircular wire frame as shown in the figure. 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 $BOC={75}^{\circ },$ where $O$ is the center of the semicircular arc. The speed of bead $B$ at that instant is:

• A. $\sqrt{2}u$
• B. $u$
• C. $\frac{u}{2\sqrt{2}}$
• D. $\sqrt{\frac{2}{3}}u$

Answer 1

The correct option is A $\sqrt{2}u$

As the string always remains tight, it may be considered as a rigid body and their is not relative motion between the points along the length of the string.

Thus the components of $v$ and $u$ along the string should remain same

$ucos{45}^o=vcos{60}^o$

or
$v=\sqrt{2}u$