A disk of radius R with uniform positive charge density `sigma` is placed on the xy plane with its center at the origin. The Coulomb potential along the z-axis is
` V(z) = sigma/(2epsilon_(0)) (sqrt(R^(2))+z^(2)-z)`.
A particle of positive charge ? is placed initially at rest at a point on the z axis with ?`z = z_(0) and z_(0) gt 0` . In addition to the Coulomb force, the particle experiences a vertical force `vec(F) = - c hat(k) " with "c gt 0` . Let`beta = (2cepsilon_(0))/(qsigma)` Which of the following statement(s) is(are) correct?

Options

A. For `beta = 1/4 and z_(0) = 25/7` , the particle reaches the origin
B. For `beta = 1/4 and z_(0)=3/7` R , the particle reaches the origin.
C. For `beta = 1/4 and z_(0)=R/(sqrt(3))` the particle returns back to `z=z_(0)`
D. For `beta gt 1 and z_(0) gt 0 ` ,the particle always reaches the origin.