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

Options

A. `mg//2`
B. `sqrt(3)mg`
C. `3sqrt(3)mg`
D. `(3sqrt(3)mg)/(2)`

Answer

D

Explanation

`x=AB-R`
`2Rcosu30^(@)-R=(sqrt(3-1))R` Spring force
`F=kx`
`=((sqrt(3+1)mg))/(R)xx(sqrt(3-1))R=2mg` From figure `N=(F+mg)cos30^(@)=(sqrt(3)mg)/(2)` .