A charged particle of mass `m_(1) ` and charge `q_(1)` is revolving in a cricle of radius r. another charged particle of charge `q_(2)` and mass `m_(2)` is situated at the centre of the circle. If the velocity and time period of the revolving particle be v and T respectively, then,

Options

A. `v=sqrt((q_(1)q_(2)r)/(4pi epsi_(0) m_(1)))`
B. `v=(1)/(m_(1)) sqrt((q_(1)q_(2))/(4pi epsi_(0) m_(1)))`
C. `T=sqrt((16 pi^(3) epsi_(0)m_(1)^(2)r^(3))/(q_(1)q_(2)))`
D. `T=sqrt((16 pi^(3) epsi_(0)m_(2)r^(3))/(q_(1)q_(2)))`

Explanation

Here, both `q_(1) and q_(2)` are either positive or negative.
Thus, `(m_(1)v^(2))/(r)=(1)/(4 pi epsi_(0))*(q_(1) q_(2))/(r^(2))= or, v= sqrt((I)/(4 pi epsi_(0) m_(1))*(q_(1)q_(2))/(r))`
Now, time period `T=sqrt((16 pi^(3) epsi_(0) m_(1) r^(3))/( q_(1)q_(2))) [ :. v= r omega and omega =(2pi)/(T)]`
Hence, nonoe of the options is correct.