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  4. 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.

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Q. 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.Physics Question Image

UPSEEUPSEE 2016

Solution:

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