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.

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., R, 2 R, 3 R 2, 5 R 2

MARKS App · 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 ) + 1 2 m ( 0 ) 2 = m g H + 1 2 m ( 0 ) 2 ⇒ m g 2 R = m g H ⇒ 2 R = H ⇒ H = 2 R

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