Question

A bead is free to slide down a smooth wire tightly stretched between points $A$ and $B$ on a verticle circle of radius $R$. If the bead starts from rest at '$A$', the highest point on the circle, its velocity when it arrives at $B$ is

• A. $2\sqrt{gR}$
• B. $2\sqrt{gR}\cos \theta$
• C. $\frac{2\sqrt{R}}{g}$
• D. None of the above

Answer 1

Answer: (B)

$2\sqrt{gR}\cos \theta$

$a=g\cos \theta AB=2R\cos \theta \Rightarrow v^2=u^2+2as{v}^2=0+2\left(g\cos \theta \right)2R\cos \theta \Rightarrow v^2=4gR{\cos }^2\theta \Rightarrow v=2\sqrt{gR}\cos \theta$