Question

A small bead of mass $M$ slides on a smooth wire that is bent in a circle of radius $R$. It is released at the top of the circular part of the wire (point $A$ in the figure) with a negligibly small velocity. Find the height $H$ where the bead will reverse direction :

• A. $R$
• B. $2R$
• C. $\frac{3R}{2}$
• D. $\frac{5R}{2}$

Answer 1

The correct option is B $2R$

Key Point Apply conservation of energy at two different position of the object.
According to energy conservation between points $A$ and $B$
$mg\left(2R\right)+\frac{1}{2}(0{)}^2=mgH+\frac{1}{2}m(0{)}^2$
$\Rightarrow mg\left(2R\right)=mgH$
$\Rightarrow 2R=H$
$\Rightarrow H=2R$