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JEE Advanced 2022 Paper 2

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Question : 30

Total: 54

A disk of radius R with uniform positive charge density σ is placed on the xy plane with its center at the origin. The Coulomb potential along the z-axis is
V(z)=‌

(√R2+z2−z)
A particle of positive charge q is placed initially at rest at a point on the z axis with z=z0 and z0>0. In addition to the Coulomb force, the particle experiences a vertical force

with c>0. Let β=‌

Which of the following statement(s) is(are) correct?

For β=‌
1
4
and z0=‌
25
7
R, the particle reaches the origin.
For β=‌
1
4
and z0=‌
3
7
R, the particle reaches the origin.
For β=‌
1
4
and z0=‌
R
√3
, the particle returns back to z=z0.
For β>1 and z0>0, the particle always reaches the origin.

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