A Circular ring of radius `3a` is uniformly charged with charge `q` is kept in `x-y` plane with center at origin. A particle of charge `q` and mass `m` is projected frim `x=4` towards origin. Find the minimum speed of projection such that it reaches origin.

Options

A. `sqrt(2/m)(1/15 q^2/(4pi in_0a))^(1//2)`
B. `sqrt(2/m)(2/15 q^2/(4pi in_0a))^(1//2)`
C. `sqrt(2/m)(4/15 q^2/(4pi in_0a))^(1//2)`
D. `sqrt(2/m)(1/5 q^2/(4pi in_0a))^(1//2)`

Answer

B

Explanation

From energy conversation,
`U_(i)+k_(i)=U_(f)+k_(f)`
`(k(q)(q))/(sqrt((3a)^(2)+(4a)^(2)))+(1)/(2)mv_(min)^(2)=(k(q)(q))/(3a)+0rArrV_(min)=sqrt((2)/(m))((2)/(15)(q^2)/(4piin_(0)a))^(1//2)`