A bead of mass \(100 \mathrm{~g}\) is attached to one end of a spring of natural length \(L\) and spring constant \(k=\frac{(\sqrt{3}+1) m g}{L}\), where \(m\) is the mass of bead. The other end of the spring is fixed at point \(A\) on a smooth vertical ring of radius \(R\) as shown in the figure. The normal reaction at \(B\) just after it is released to move is (take, \(g=9.8 \mathrm{~ms}^{-2}\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.