Question

A bead of mass $m$ is attached to one end of a spring of natural length $R$ and spring constant $k=\frac{(\sqrt{3}+1)mg}{R}$. The other end of the spring is fixed at point $A$ on a smooth vertical ring of radius $R$. Then normal reaction at $B$ just after it is release to move is

• A. $\frac{mg}{2}$
• B. $\sqrt{3}mg$
• C. $3\sqrt{3}mg$
• D. $\frac{3\sqrt{3}mg}{2}$

Answer 1

The correct option is D $\frac{3\sqrt{3}mg}{2}$

$\begin{array}{c}x=\left(2R\cos 3o^o-R\right)\\ =R\left[\sqrt{3}-1\right]\\ \therefore N=mg\cos {30}^o+Kx\cos {30}^o\\ N=mg.\frac{\sqrt{3}}{2}+\frac{\left(\sqrt{3}+1\right)mg}{R}.R\left(\sqrt{3}-1\right).\frac{\sqrt{3}}{2}\\ N=\frac{\sqrt{3}mg}{2}+\sqrt{3}mg=\frac{3\sqrt{3}mg}{2}\\ Hence,\\ optionDiscorrectanswer.\end{array}$