The normal force on the bead at point A is 1 N.
According to the Law Of Conservation of Energy, the total energy of the bead at the topmost point of height of 3.50 R is the same as its total energy at point A.
The energy at a height of 3.50R is equal to its potential energy which is
U= mgh= mg x 3.5R= 3.5mgR .........(i)
The energy at point A is,
E= mg(2R)+ 1/2 mv^2 ...........(ii)
Now, equating (i) and (ii)
3.5mgR = 2mgR + 1/2 mv^2
3.5mgR - 2mgR = 1/2mv^2
1.5gR = 1/2 v^2
3gR = v^2
V = √3gR
At point A, three forces are there weight of the bead(mg), normal reaction(N), and centripetal force(mv^2/r).
Balancing these forces,
mg + N = mv^2/r
N= mv^2/r - mg
Putting the given values in the above equation, we get the normal reaction
N= 1 N
Thus, the normal force on the bead at point A is 1N.
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