Question

A bead of mass m is attached to one end of a spring of natural length R and spring constant k = √(3 + 1)mg/R . The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown in figure. The normal reaction at B just after it is released to move is

(A)  mg/2 

(B)  √3 mg

(C)  3√3 mg

(D)  3√3  mg/2

Answer 1

Correct option  (D)  3√3  mg/2

Explanation:

The extension is spring is x = 2R cos 30° – R = (√3 - 1) R

Applying Newton's second law to the bead normal to circular ring at point B