Question

A bead can slide on a smooth circular wire frame of radius $r$ which is fixed in a vertical plane.The bead is displaced slightly from the highest point of the wire frame. The speed of hte bead subsequently as a function of the angle $\theta$ made by the bead with the vertical line is

• A. $\sqrt{2gr}$
  
• B. $\sqrt{2gr(1-sin\theta )}$
  
• C. $\sqrt{2gr(1-cos\theta )}$
  
  
• D. $\sqrt{2gr}$
  

Answer 1

The correct option is C $\sqrt{2gr(1-cos\theta )}$



Clearly, $h=r(1-cos\theta )$



Now, Using energy conservation principle,

Decrease in PE $=$ Increase in KE

or, $mgr(1-cos\theta )=\frac{1}{2}m{v}^2-0$

or, $v=\sqrt{2gr(1-cos\theta )}$

Hence, option $\left(c\right)$ is the correct answer.