A Bead of mass `m` is attached to one end of a spring of natural length `'R'` and spring cosntant `'k=((sqrt3+1)mg)/R'`. The other end of the spring is fixed at point `'A'` on a smooth vertical ring of radius `'R'` as shown

Options

A. The normal reaction at `'B'` just after the bead is released to move is:`(3sqrt(3)mg)/2`
B. The tangential acceleration of the bead just after it is released to move is :`g//2`
C. The normal reaction at `'B'` just after the bead is released to move is :`(3mg)/2`
D. Just after the bead is released to move the normal acceleration and Tangential acceleration are numerically equal.

Answer

A, B, C

Explanation

Force developed in the spring due to elongation is :`F_(s)=Kx=K(2R cos 30-R)`
`=KR(sqrt3-1)=((sqrt3+1)mg)/Rxx(sqrt3+1)=2mg`
Normal reaction`N=F_(s)cos30+mg cos30`
`=3mg cos 30=(3sqrt3mg)/2`
Tangential force `F_(T)=F_(S) sin 30-mg sin 30`
`=mg sin 30=ma_(T)`
`a_(T)=g//2`