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 velocit

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.

TestHub · Accepted Answer

Apply conservation of energy at two different positions of the object.

According to energy conservation between points A and B

$m g (2 R) + \frac{1}{2} m {(0)}^{2} = m g H + \frac{1}{2} m {(0)}^{2}$

$\Rightarrow m g (2 R) = m g H$

$\Rightarrow 2 R = H$

$\Rightarrow H = 2 R$

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