Question

A particle of charge –q and mass m moves in a
circular orbit around a fixed point charge +Q in a
circle of radius r and time period T. Which of the
following may be correct?
(1) p « T2
(2) poc
T3/2
(3) pa T2/3
(4) po T3​

Answer 1

r³∝T² is correct answer .

Explanation

Fe= k(q)Q/r² (direction toward particle)

Where, Fe is force of electrostatics

But , from newton's second law force = ma

So, mac = k(q)Q/r²

where, ac is centriputal acceleration ,

ac = ω²r

⟹ mω²r = kqQ/r²

⟹ m(2π/T)² r = kqQ /r² -- (∵ ω = 2π/T)

⟹ m(4π²/T²)r = kqQ/r²

⟹ r³ = (kqQ/m4π²)T²

∴r³∝ T² Is correct answer .