Two concentric rings placed in a gravity free region in yz-plane one of radius R carries a + Q and second of radius 4R and charge –8Q distributed uniformly over it. Find the velocity with which a point charge of mass m and charge +q should be projected from a a distance 3R from the centre of rings on its axis so that it will reach to the centre of the rings.

Two concentric rings placed in a gravity free region in yz-plane one o

1.	Two concentric rings placed in a gravity free region in yz-plane one of radius R carries a + Q and second of radius 4R and charge –8Q distributed uniformly over it. Find the velocity with which a point charge of mass m and charge +q should be projected from a a distance 3R from the centre of rings on its axis so that it will reach to the centre of the rings.
Answer» SOLUTION :From ENERGY conservation PRINCIPLE `K_i+U_i=K_f+U_f` `or 1/2mv^2+(+Q)V_i=0(+q)V_f` or `v=sqrt((2q)/m(-V_i+V_f))` `sqrt((2a)/m[(-Q)/(sqrt(10)R)+(8Q)/(5R)+Q/R-(8Q)/(4R)] 1/(4piepsilon_0))` `=sqrt((Qq)/(2piepsilon_0mR) ((3sqrt(10)-5)/(5sqrt10)))`

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