Question:

A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from the line charge, is proportional to:

v∝√r/r0

v∝√ln(r/r0)

v∝√(r/r0)

Correct option is D. v∝√(r/r0)

1/2mv² = -q(Vf - Vi)
E = λ/2πε₀r
ΔV = λ/2πε₀ ln(r₀/r)
1/2mv² = -qλ/2πε₀ ln(r₀/r)
v ∝ √ln(r/r₀)