Correct Answer - `(5)`
According to conservation of energy between A and B, loss in gravitational potential energy=gain in elastic potential energy + gain in KE
`mg(r/2+r)=1/2k(2r-r)^2+1/2mv^2` (i)
At point B, centripetal force equation is
`kr-mg=(mv^2)/(r)` (ii)
Solving Eqs. (i), and (ii), we get `k=500Nm^-1`