A charge `q` of mass `m` is projected form a long distance with speed `v` towards another stationery particle of same mass and charge the distance of closet approach of the particles is

Options

A. `(q^(2))/(2piepsilon_(0)mv^(2))`
B. `(2q^(2))/(piepsilon_(0)mv^(2))`
C. `(3q^(2))/(2piepsilon_(0)mv^(2))`
D. `(q^(2))/(piepsilon_(0)mv^(2))`

Answer

D

Explanation

As the first particle approaches the second due to repulsion it recedes away from it along the same line of approach.The seperation between them is minimum when their velocities are equal .Applying conservation of linear momentum
`mv=mv_(f)+mv_(f) v_(f)=V//2`
`rArr (1)/(2)mv^(2)=(1)/(2)(m+m)v^(2)f+(q^(2))/(4piepsilon_(0)r)`
`(1)/(2)mv^(2)=(1)/(2)2m(v^(2))/(4)+(q^(2))/(4piepsilon_(0)r)(1)/(4)mv^(2)=(q^(2))/(4piepsilon_(0)r)`
`r=(q^(2))/(piepsilon_(0)mv^(2))`